I/CONSECUENCIAS_DE_LA_CONTINUIDAD_GRUPO_7.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [
        "m7fIHBMyr-GT"
      ]
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#<font color = 9ACD32> **TALLER CONSECUENCIAS DE LA CONTINUIDAD**\n",
        "---\n",
        "**Grupo 7:**\n",
        "* Mariana Agudelo\n",
        "* Juan José De la Pava\n",
        "* David Esteban Dulce\n",
        "* Rony Farid Ordoñez\n",
        "---\n"
      ],
      "metadata": {
        "id": "qgmn31hVakLO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "----\n",
        "#<font color = 9ACD32>1.</font>\n",
        "Use the bisection algorithm to approximate a solution to each of the following\n",
        "equations on the given interval. Your answer should have an error of no more\n",
        "than $ 0.005 $.\n",
        "\n",
        "a. $ x^2 - 2 = 0 $ on $ [0,4] $\n",
        "\n",
        "b. $ x^5 − 6x^3 + 2x = 2 $ on $ [0,4] $\n",
        "\n",
        "c. $  cos(x) = x $ on $ [0, π] $\n",
        "\n",
        "d. $ x^2 - 2 = 0 $ on $ [0,4] $"
      ],
      "metadata": {
        "id": "FJrqZY19yPRr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "\n",
        "# minimum iterations to find the root within an error bound\n",
        "def errorBound(a, b, err):\n",
        "    iteration = np.log((b - a) / err) / np.log(2)\n",
        "    return int(np.ceil(iteration))\n",
        "\n",
        "def bisection(function, interval):\n",
        "    \"\"\"\n",
        "    param function: find root for function\n",
        "    param interval: list with interval[0] as start point and interval[1] as end point\n",
        "    return root\n",
        "    \"\"\"\n",
        "\n",
        "    x0 = interval[0]\n",
        "    x1 = interval[1]\n",
        "\n",
        "    # intermediate value theorem\n",
        "    if not ((function(x0) * function(x1)) < 0):\n",
        "        print(f\"{interval} is not a valid interval\")\n",
        "\n",
        "    # iterations required to find the root within a specified error bound\n",
        "    iteration = errorBound(x0, x1, 0.005)\n",
        "\n",
        "    root = x0 + ((x1 - x0) / 2.0)\n",
        "\n",
        "    # evaluate y at current estimated root\n",
        "    y = function(root)\n",
        "\n",
        "    # check tolerance condition\n",
        "    while not (-0.005 <= y <= 0.005):\n",
        "\n",
        "        # check what the next interval will be\n",
        "        if function(root) < 0:\n",
        "            x0 = root  # [root, x1]\n",
        "        else:\n",
        "            x1 = root  # [x0, root]\n",
        "\n",
        "        root = x0 + ((x1 - x0) / 2.0)\n",
        "        y = function(root)\n",
        "\n",
        "    print(f\"iterations: {iteration}\")\n",
        "\n",
        "    # return root approximation\n",
        "    return root\n",
        "\n",
        "# a.  x**2 - 2 = 0, [0,4]\n",
        "a = lambda x: x**2 - 2\n",
        "print(f\"a: {bisection(a, [0,4])}\")\n",
        "\n",
        "# b. x**5 − 6x**3 + 2x -2 = 0 [0,4]\n",
        "b = lambda x: x**5 - (6*(x**3)) + (2*x) - 2\n",
        "print(f\"b: {bisection(b, [0,4])}\")\n",
        "\n",
        "# c. cos(x) - x = 0 [0, π]\n",
        "c = lambda x: np.cos(x) - x\n",
        "print(f\"c: {bisection(a, [0,4])}\")\n",
        "\n",
        "# d. x**2 - 2 = 0 [0,4]\n",
        "d = lambda x: x**2 - 2\n",
        "print(f\"d: {bisection(d, [0,4])}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0RUS4o5Va9JV",
        "outputId": "d0693523-0f1a-4455-b963-ac145c7d4a09"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iterations: 10\n",
            "a: 1.4140625\n",
            "iterations: 10\n",
            "b: 2.407958984375\n",
            "iterations: 10\n",
            "c: 1.4140625\n",
            "iterations: 10\n",
            "d: 1.4140625\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "----\n",
        "#<font color = 9ACD32>3.</font>\n",
        "Suppose if the market price for a certain product is p dollars, then the demand for that product will be\n",
        "\n",
        "$D(p) = \\frac{50000p + 10000}{p2}$\n",
        "units.\n",
        "\n",
        "At the same time, suppose that at a price of p dollars producers will be willing to\n",
        "supply\n",
        "\n",
        "$S(p) = \\frac{1}{3} p^2 + 2p\\:$ units.\n"
      ],
      "metadata": {
        "id": "oEUKHAcE5TyN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##A)"
      ],
      "metadata": {
        "id": "XFMHmz936i9q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def demanda(p):\n",
        "    return (50000*p + 10000)/p**2\n",
        "\n",
        "def oferta(p):\n",
        "    return (1/3)*(p**2) + 2*p\n",
        "\n",
        "\n",
        "precios = np.linspace(1, 100, 101)\n",
        "\n",
        "\n",
        "plt.plot(precios, demanda(precios), label='Demanda')\n",
        "plt.plot(precios, oferta(precios), label='Oferta')\n",
        "\n",
        "\n",
        "plt.xlabel('Precio (Dolares)')\n",
        "plt.ylabel('Cantidad (Unidades)')\n",
        "plt.legend()\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "wB19L0fc5s8F",
        "outputId": "a7058fb7-d3d3-4f7a-a298-d07b9aca8a99"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##B)"
      ],
      "metadata": {
        "id": "BGjz0LEj6kYi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def f(p):\n",
        "    return demanda(p) - oferta(p)\n",
        "\n",
        "\n",
        "a = 20\n",
        "b = 80\n",
        "\n",
        "epsilon = 1e-6\n",
        "\n",
        "while abs(b - a) > epsilon:\n",
        "    c = (a + b)/2\n",
        "    if f(a)*f(c) < 0:\n",
        "        b = c\n",
        "    else:\n",
        "        a = c\n",
        "\n",
        "cero = (a + b)/2\n",
        "\n",
        "print('El precio de equilibrio es:', cero)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6oRSL7Xd6lfp",
        "outputId": "9c614914-4801-4594-97d2-d002164155d7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "El precio de equilibrio es: 51.27522453665733\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##C)\n",
        "Para encontrar la cantidad de unidades que se desea producir, se remplaza el precio en la cantidad de demanda."
      ],
      "metadata": {
        "id": "8GZX0MyE7pZU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"El productor va a querer desarrollar {demanda(cero)} unidades cuando el precio es {cero}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9wT3gCQ471Ox",
        "outputId": "423b7b4a-c70c-44b1-e8e8-00e590f03026"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "El productor va a querer desarrollar 978.9333233688795 unidades cuando el precio es 51.27522453665733\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##D)\n",
        "Si los productores subieran el precio por encima del precio de equilibrio, la cantidad ofrecida superaría la cantidad demandada, lo que daría lugar a un excedente de oferta. Este excedente ejercería una presión a la baja sobre el precio, lo que finalmente haría que retrocediera hasta el precio de equilibrio.\n",
        "\n",
        "Si los productores bajaran el precio por debajo del precio de equilibrio, la cantidad demandada excedería la cantidad ofrecida, lo que provocaría una escasez del producto. Esta escasez ejercería una presión al alza sobre el precio, lo que eventualmente haría que volviera a subir al precio de equilibrio."
      ],
      "metadata": {
        "id": "PcdL-9rH8b9v"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##E)\n",
        "Si los productores aumentan la producción, el nuevo precio y la cantidad de equilibrio pueden aumentar o disminuir según la relación entre las nuevas curvas de oferta y demanda. Si los productores reducen la producción, el nuevo precio y la cantidad de equilibrio también pueden aumentar o disminuir según la relación entre las nuevas curvas de oferta y demanda."
      ],
      "metadata": {
        "id": "gcAwjRqn9-m5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "---\n",
        "#<font color = 9ACD32>5.</font>\n",
        "When a potter sells his pots for $p$ dollars a piece, he can sell $D(p) = 750 − 50p$ of them. Suppose the pots cost him $5.00 a piece to make. What price should the\n",
        "potter charge in order to maximize his profit?"
      ],
      "metadata": {
        "id": "m7fIHBMyr-GT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Tenemos los siguientes datos:\n",
        "\n",
        "* Costo por artículo: $5\n",
        "\n",
        "* Cantidad vendida: $Q=D(p)=750-50p$\n",
        "\n",
        "* Ingreso total: $p×Q$\n",
        "\n",
        "* Costos de producción: Costo artículo * cantidad vendida → $5Q$\n",
        "\n",
        "* Ganancias (profit) = ingreso total - costos de producción\n",
        "\n",
        "Ganancias:\n",
        "\n",
        "$G(p)=pQ-5Q\\:=\\: -50p^2+1000p-3750$ → Función cuadrática (Función polinómica: es *continua*)\n",
        "\n",
        "**Gráfica:**"
      ],
      "metadata": {
        "id": "2svX5WgKov4p"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def profit(p):\n",
        "    return -50*p**2 + 1000*p - 3750\n",
        "p=np.linspace(5, 15, 100)\n",
        "\n",
        "plt.plot(p, profit(p), 'g', label=\"Ganancias\")\n",
        "plt.plot(10,1250,'.b', label=\"Ganancias máximas v(10,1250)\")\n",
        "plt.title('Ganancias en función del precio')\n",
        "plt.xlabel('Precio (Dolares)')\n",
        "plt.ylabel('Cantidad de ganancias hechas')\n",
        "plt.axhline(y=1250, xmin=0, xmax=1, linestyle='--', label=\"Límite\")\n",
        "plt.grid(color=\"grey\", linestyle=\"--\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "wtYxK9zIgBsP",
        "outputId": "305bf25f-757a-49d6-873c-8f5f27105436"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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A5cqVad68OQkJCQCEhYXRq1cvpk6dSnJyMgDdu3dny5YtbN26FYAWLVoQEhLCwoULAahWrRoNGjRg4sSJAERERAAwadIkTpywTfzp2bMna9asYceOHQC0atWK1NRUli5dCkDNmjWJjo5m8mTbx1i8eHG6devGhAkTOHPmDABxcXEsW7aMXbtsk6XatWvHyZMnWbFiBQAxMTFUqVKFadOmAVCqVCk6d+5MQkICKSm2YaHx8fHMmzePv//+G7DF6U9KSrJH1YyNjSUqKso+Y7Vs2bJ07NiRsWPHkpaWRlBQEPHx8cyaNct+A3Xq1InExEQOHz7M6NGj3VJPJ/OdZEWhFXz3+3cUkkJ0C+/Gx/d/zK7tu/j2y28drqcePXrkqZ6OHrVN/HJHPQ2sMJBqB6ox++RsPlnzCWPXj6VlgZa0K9SOylGVHa6ndetsE7ZyW0+nT5+235Puup/yWk95vZ8OHz7M9OnT3Xo/5bWessOlQ2etlsUstfosMqQ/B9QH7lRVFZERwCpVnWAdHwf8ZJ3eXlXjrfT7gEaqOiC7cn21z+Lff//lmmvc/6/Pk7hD84nzJ3h12at8uOpD8ofkZ0iTIQxqMoiI/BEuLTcrPFXPO47s4IXFLzB562TKhpflzVZv0rN2T4LE9R2x5rvtG2TXZ+H27noRicPW8d1T//NU+4FrM5wWZaVlle6XJCZeGerA33GlZlXl681fU214Nd5Z8Q69avdix4AdvNjyRY85CvBcPVcrUY1J3SbxywO/UDa8LPdPv58bP7+RTf9ucnnZ5rvt+7jVWVgjm54G7lDVMxkOzQR6iEh+EakEVAVWA2uAqiJSSURCgR7WuX5JehMykHCV5l1Hd9F+Ynt6fteT8kXKszp+NZ93+pwy4Z4Pm+Hpem56bVN+jf+V8Z3G81fyX8SOjmXogqGcuXAm54tziac1ewJ/0+wyZyEi3wArgetFJFFEHgRGAOHAfBHZICKfAajqVuBbbB3Xc4BHVfWiqqYCA4C5wO/At9a5BkOmpGkaH636iOhPo1mxbwUft/+YlQ+upEG5nCfBBRJBEkRcnTh+f/R37qt9H2/98ha1R9Zm+d7lnjbN4K1kNUzKlzdfHTr722+/edoEt+NMzbuP7taWCS2VYWiHiR103/F9TsvbmXhjPS/evVgrf1RZZZjokLlD9OyFs07N3xs1uxpf1Ew2Q2f9a4qhjxMZGXiTp5yl+auNX1F7ZG3WHVjHuDvG8cM9PxAV4Z2Lz3hjPbes2JKN/TfyUOxDvLvyXWJHxzq1L8MbNbsaf9NsnIUXkT7MLZDIq+ZTKafoPb0390+/nzql67Dp4U08UPcBr47I6q31XDi0MCM7jmROzzkkn02m4ZiGfLb2s/QJtXnCWzW7En/TbJyFwWfZ+M9G6o2qx4RNExjWYhiLey+mYtGKnjbL52lXpR0b+2/k5ko38/Dsh7lryl0cP3fc02YZPIxxFl5E+fLlPW2C28mt5gmbJtB4XGNOXzjNovsX8WLLF70+THc6vlDPpQqVYva9s3m79dvM2D6DBmMasPVQ7seW+IJmZ+Nvms16Fl5E+uzMQOJqNadcTOHJuU8yYs0IWlRoweRukz0SviIv+Fo9L9+7nLum3MWplFN83ulz7q5591Xn4WuanYEvavaqSXmGrEmfih9IXI3mI2eO0PartoxYM4LBjQcz/775PucowPfquVmFZqx/aD0xpWPoPrU7zy18jjS9urUafE2zM/A3zcZZGHyCPw7/QaOxjViVuIoJXSbwXrv3yBecz9NmBQxlw8uyuPdi+tbry+s/v87dU+526SQ+g/dhFj/yIvxtgXdHcETzgl0L6PZtN/KH5Gdx78U0uTaH9Ui9HF+t59DgUEZ1HMUNJW/gyXlPsufYHmbeM5Oy4WVzvtZHNecFf9Ns+iwMXs2ETRPoM6MPN5S8gR/u+YEKRSt42iQDMHvHbHpM60GJgiWY02sO1UtW97RJBidg+ix8hOnTp3vaBLeTlWZV5e1f3ua+7++jWflmLO+z3G8chT/Uc4dqHVjSewlnU89y4+c3smLfimzP9wfNV4u/ab4qZyEixUSktquMCXTS48oHEplpTtM0Bs8dzDMLnqFHdA9+6vkTRQoU8YB1rsFf6jm2bCwrH1xJiYIlaPVlK37Y/kOW5/qL5qvB3zTn6CxEZImIRIhIcWA9MEZE3ne9aYZA5GLaReJnxvPhrx/yeKPHmXjnRJ9ZBzsQqVysMr888AvRpaLpMrkL32z+xtMmGVxEjn0WIvKbqtYVkXjgWlV9UUQ2qarXtjB8tc/iyJEjlChRwtNmuJWMmlMuptDru15M2TaFYS2G8UKLF7w6bEdu8cd6PnH+BLd/czvL9y7ns46f0S+23yXH/VFzTvii5rz2WYSISBngbmCWUy0zXMLOnTs9bYLbSdd8LvUcd06+kynbpvBe2/d4seWLfukowD/rOSJ/BD/1/In2Vdrz0KyH+HDVh5cc90fNOeFvmh1xFi9jW09ip6quEZHKwJ+uNSswSV9LOpDYuHGj3VHM/nM2n3X4jMFNBnvaLJfir/Ucli+M6T2mc+cNdzJo7iA+WPmB/Zi/as4Of9Oc4zwLVZ0CTMmwvwvIfmVvg8FBLugFukzuwpydcxjdcTR9Y/t62iRDHggNDmVS10ncM+0eBs+zOf1BTQZ52CqDM8jRWYhIAeBBoCZQID1dVR9woV0BSdOmTT1tgls5n3qeSTqJn3f+zJjbxxBfL97TJrkFf6/nfMH5+KbrN9z73b0MnjcYEaF109aeNsvt+Fs9O/IY6iugNNAOWApEASddaVSgEh4e7mkT3EZqWir3TLuHn//9mdEdRweMo4DAqOd8wfn4+s6v6XpDVwbNHcSsg4HX3elv9eyIs6iiqv8DTqvqF0AHoJFrzQpM5s6d62kT3EKaptFnRh++/+N77o64O+AePQVKPecLzsfXXb/m1iq38uyKZ/l689eeNsmt+Fs9O+IsLlivx0QkGigClHKdSQZ/RlV5dPajTNg0gddueY1WhVp52iSDCwkNDmXa3dOoGlqV+7+/n+l/TPe0SYZc4oizGC0ixYD/ATOBbcDbLrUqQKlcubKnTXA5Ly55kc/WfcbQG4fybLNnA0Lz5QSa5oL5CvJO3XeoX7Y+Pab2YNneZZ42yS34Wz2bQIJeREpKit9FqszIJ6s/YcBPA4ivG8/o20cjIn6vOTMCVfPJ1JPcNP4mDp48yLI+y6h9jdfO63UKvljPeZqUJyL5ReReEXlWRF5I35xvpiEhIcHTJriMKVun8NhPj9Hp+k6M7DjSPuHOnzVnRaBqLhFWgrm95lI4tDDtJ7Rnz7E9njbLpfhbPTvyGGoG0AlIBU5n2LJFRD4XkUMisiVDWnERmS8if1qvxax0EZGPRWSniGwSkXoZrultnf+niPS+WoEGz7Ns7zJ6fd+LG8vfyDddvyEkyCyjEqiUL1Keub3mcjb1LO0ntCf5bLKnTTI4iCPOIkpVu6vq26r6XvrmwHUJQPvL0oYCC1W1KrDQ2ge4Fahqbf2AkWBzLsCL2EZfNQReTHcw/khYWJinTXA62w9vp/OkzlQuVpmZPWZSMF/BS477o+acCHTNNUvVZGaPmew+tpsuk7twPvW8By1zHf5Wz44EEhwNDFfVzVeduUhFYJaqRlv724GWqnrQije1RFWvF5FR1vtvMp6XvqnqQ1b6Jedlha/2WfgbSaeTaDyuMadSTrHqwVVUKlbJ0yYZvIivN39Nz+960rNWT77q8pXfxgLzJbLrs8jyeYCIbAbUOqePiOwCzgMCaC6jzl6jqget9/8A11jvywH7MpyXaKVllZ6Zvf2wtUooXbo0o0ePBqBhw4ZERkYye/ZsAMqXL0/btm3ti6mHhoYSFxfH9OnT7fHnu3btys6dO+2xXZo2bUp4eLh93HTlypVp3ry5/ZlkWFgYvXr1YurUqSQn25rV3bt3Z8uWLWzduhWAFi1aEBISwsKFCwGoVq0aDRo0YOLEiQBEREQQEhJCamoqJ06cAKBnz56sWbOGHTt2ANCqVStSU1NZunQpADVr1iQ6OprJkycDULx4cbp168aECRM4c8a2PnJcXBzLli1j165dALRr146TJ0+yYoVtsZqYmBiqVKnCtGnTAChVqhSdO3cmISGBlJQUAOLj45k3bx5///03AB06dCApKYnVq1cDEBsbS1RUFDNmzACgbNmytG7fmsYfNWbfhX0MiRxCpWKVmDVrFgcOHACgU6dOJCYmsmDBAooVK+ZT9dSjRw8mTZqU63o6ffo0gwYN8op66tixI2PHjiUtLY2goCDi4+Mzrad169YBub+fpk6dancG6fV0auUpOoV3YuLmiVSIqECFXRW8qp7yej8dPXqU66+/3qfqKVtUNdMNqJDdltV1l+VREdiSYf/YZcePWq+zgJsypC8E6gNDgOczpP8PGJJTubGxseqLjBo1ytMmOIW0tDTtOa2nMgydtm1atuf6i+arwWj+j7S0NH1g+gPKMPTrTV+72SrX4ov1DKzVLH5Xs+yzUNW9qroXKAMkZ9g/ii38R27413r8hPWavpTUfuDaDOdFWWlZpRu8mLd+eYuJmyfy2i2vcecNd3raHIMXIyKM7DiSZuWb8cDMB1izf42nTTJkRVZeRP/7N/8bVt+GtR8ErM/pOs28ZfEOMNR6PxR423rfAfgJ2yOuxsBqK704sBsoZm27geI5leurLYtjx4552oQ8M/336SrDRO+Zeo+mpaXleL4/aL5ajOYrOXTqkFb8sKKWebeMJh5PdJNVrsUX65nctCwyIFYm6c4lDcei1X4DrASuF5FEEXkQeBNoIyJ/Aq2tfYAfgV3ATmAM8IhVVjLwCrDG2l620vySLVu25HySF7Pl0BZ6fteT+mXrM+6OcQ51WPq65txgNF9JZKFIZvaYycmUk3SZ3IVzqefcZJnr8Ld6dsRZ7BKRgSKSz9oex/bDni2qeo+qllHVfKoaparjVPWIqrZS1aqq2jr9h99yao+q6nWqWktV12bI53NVrWJt43Mv1ftJ77zzRY6dO0aXyV0Izx/O9B7TrxgimxW+rDm3GM2ZU+uaWnzV5SvWHFjDo7MfJcN/VJ/E3+rZEWfRH2iKra8gEduch37ZXmEIKNI0jZ7f9WTPsT1MvWsqZcPLetokg4/SuXpnnm/2PJ9v+JxR60Z52hxDBhxZKe8Q0MMNtgQ8LVq08LQJueKlJS/x458/8sltn3Bj+Ruv6lpf1ZwXjObsGdZyGOv/Wc/AnwZS+5raNL3WNxcR8rd6diQ2VDURWZgetkNEaovI8643LfAICfG9MBizd8zm5WUvE1cnjofrP3zV1/ui5rxiNGdPcFAwE7pMoHyR8nT7thv/nvrXhZa5Dn+rZ0ceQ40B/g9rXQtV3YRpabiE9AlGvsKeY3u47/v7qFO6Dp/e9mmuZuD6mmZnYDTnTLGCxfi++/ccPXeUe7+7l4tpF11kmevwt3p2xFmEqerqy9JSXWGMwXc4n3qeu6bcRZqmMfWuqQ53aBsMjlLrmlp8etunLNq9iGFLhnnanIDHEWdxWESuwxb6AxHpBhzM/hJDbqhWrZqnTXCYJ+c9ydoDaxnfaTzXFb8u1/n4kmZnYTQ7Tp+6fehTpw+vLn+VOTvnONkq1+Jv9exIIMHKwGhsI6KOYpsY10tV97jculziq4EET58+TaFChTxtRo5M2TqFu6fezeDGg3mvnSMBiLPGVzQ7E6P56jhz4QyNxzbmwMkDbOy/kXIRmYaH8zp8sZ7ztPiRqu5S1dZAJFBdVW/yZkfhy6QHQfNmdh/dTd8f+tKoXCPebP1mzhfkgC9odjZG89URli+MKXdN4VzqOXp+19Nn+i/8rZ4dXikPeBwYZFbKC1wuXLzAPdPuQVG+6foN+YLzedokQ4Bwfcnr+eS2T1i6dymvLX/N0+YEJC5bKc9w9URERHjahGz53+L/8ev+Xxl7+1inrU3h7ZpdgdGcO+6PuZ9etXvx0tKXWLZ3mROsci3+Vs+O9FlsUWvxIl/BV/ssvJkFuxbQ5qs29K3Xl9G3j/a0OYYA5eT5k9QbXY9zqefY2H8jxQsW97RJfkWe+iyAFSJSy8k2GTJh0qRJnjYhU46cOULv6b25oeQNfNj+Q6fm7a2aXYnRnHvC84czqesk/jn1D/1n9ffq+FH+Vs9ZOgsR2Swim4CbgPUisl1ENmVINziZ9BW9vAlVpd+sfiSdTmLinRMJy+fcdYW9UbOrMZrzRmzZWF65+RWmbJvCV5u+clq+zsbf6jm7+egd3WaFwWtJ2JDAd79/x1ut36JumbqeNsdgAOCppk/x086fGPDjAJqVb2bWd3cDOfZZ+CK+2mfhbeOy/0r+izqj6lC/bH0W3LeA4KBgp5fhbZrdgdHsHPYe20vMZzHULFWTpXFLCQnyrlhMvljPee2zMLiJNWu8Z0nJi2kX6T29N8ESzJedv3SJowDv0uwujGbnUKFoBT7t8Ckr9q3g3RXvOj3/vOJv9WychRexY8cOT5tg54NVH/DLvl8Yfutwri1ybc4X5BJv0uwujGbncU/0PXSr0Y0XFr/A5n83u6SM3OJv9ezIpLxCIhJkva8mIneIiJmN5cdsPbSV5xY9R+fqnelVu5enzTEYskREGNlhJMUKFuP+6feTcjHF0yb5LY60LJYBBUSkHDAPuA9IcKVRgUqrVq08bQIXLl7g/un3E5E/glEdR+Uq7PjV4A2a3Y3R7FxKhpVkzO1j2PDPBl5Z+orLyrla/K2eHXEWoqpngDuBT1X1LqCma80KTFJTPR/5/Y2f32D9wfWM6jiKUoVKubw8b9Dsboxm53PH9XfQO6Y3b/z8BmsPeMfgFn+rZ4echYg0AXoCs6001/R2BjhLly71aPmb/93Mq8tepUd0D+684U63lOlpzZ7AaHYNH7X/iNKFS9NnRh+veBzlb/XsiLN4HNtKed+r6lYrZPli15plcDepaak8MPMBihYoyvBbh3vaHIPhqilSoAifdfyMLYe28NoyE2zQ2TgSonyZqt6hqm9Z+7tUdWBeChWRQSKyVUS2iMg3IlJARCqJyK8islNEJotIqHVufmt/p3W8Yl7K9mZq1vTc0733V77P2gNrGXHbCEqGlXRbuZ7U7CmMZtfRsVpHetXuxes/v87Gfza6pcys8Ld6dmQ0VKSIvCMiP4rIovQttwVaHeUDgfpWgMJgbGt6vwV8oKpVsC2y9KB1yYPAUSv9A+s8vyQ62jPxGrcf3s4Li1/gzhvu5K4ad7m1bE9p9iRGs2v5sN2HFC9YnD4z+nDh4gW3lXs5/lbPjjyGmgj8AVQCXgL2AHmdbRICFBSRECAM2zKttwBTreNfAJ2t952sfazjrcTVQ3Q8xOTJk91eZpqmEf9DPGH5wvjktk9cPvrpcjyh2dMYza6lRFgJPr3tU3775zfeX/m+28q9HH+rZ0fmx5dQ1XEi8riqLgWWikiunYWq7heRd4G/gbPYhuOuA46pavrwgUQgfe3EcsA+69pUETkOlAAOZ8xXRPoB/QBKly7N6NG2MNoNGzYkMjKS2bNtffPly5enbdu2jB07FoDQ0FDi4uKYPn06hw4dAqBr167s3LmTjRttzdimTZsSHh7O3LlzAahcuTLNmzcnISEBgLCwMHr16sXUqVNJTk4GoHv37mzZsoWtW7cC0KJFC0JCQli4cCFgW5+3QYMG9tW00mPfT5o0yR6ArGfPnqxZs8Y+uadVq1akpqbaO85q1qxJdHS0/UtZvHhxunXrxoQJEzhz5gwAcXFxLFu2jF27dgHQrl07Tp48yYoVKwDYVWwXP//9M/cXuZ+ZX8+kVKlSdO7cmYSEBFJSbJ2E8fHxzJs3j7///huADh06kJSUxOrVqwGIjY0lKiqKGTNmAFC2bFk6duzI2LFjSUtLIygoiPj4eGbNmsWBAwcA6NSpE4mJiRw+fJjRo0f7VD316NEjT/V09OhRgKuqp5iYGKpUqcK0adMA3F5P69atA3J/P50+fdp+T7qrnjpX78z/Fv2P1E2pRIZEuuV+ylhPhw8fZvr06T5VT9miqtluwCrrdS7QAagL/JXTddnkVwxYhG2Z1nzAdKAXsDPDOdcCW6z3W4CoDMf+AkpmV0ZsbKz6IlOmTHFreftP7NeINyL0li9u0bS0NLeWnY67NXsDRrN7SDyeqBFvRGirL1p55Pvti/UMrNUsflcdeQz1qogUAZ4EhgBjgUEOXJcVrYHdqpqkqheA74AbgaLWYymAKGC/9X6/5TywjhcBjuShfK+lW7dubi1v4E8DSbmY4pbJd1nhbs3egNHsHspFlOPNVm+ycPdCj4Qy97d6dmQ01CxVPa6qW1T1ZlWNVdWZeSjzb6CxiIRZfQ+tgG3YhuOmf7q9sS3nCjDT2sc6vsjygH7HhAkT3FbWjD9mMO33abzQ/AWqFK/itnIvx52avQWj2X08VP8hbrz2RgbPHUzS6SS3lu1v9Zzd4kdPW6/DReTjy7fcFqiqv2LrqF4PbLZsGA08AwwWkZ3Y+iTGWZeMA0pY6YOBobkt29tJfy7qak6lnGLATwOoVaoWQ5oOcUuZWeEuzd6E0ew+giSI0beP5sT5Ezw1/ym3lu1v9ZxdB/fv1qvT586r6ovAi5cl7wIaZnLuOcC94zn9nJeWvETiiUQmd5tMvmATE9Lg39SIrMFTTZ/i9Z9fp0+dPrSo2MLTJvkkZvEjLyIlJYXQ0FCXlrHp303UG1WPB+o+wOjbR7u0LEdwh2Zvw2h2P2cunKHmpzUpGFKQDf03EBrsels8rTk35GnxIxGZLyJFM+wXE5G5TrTPYLFs2TKX5p+maTw8+2GKFSzGm63fdGlZjuJqzd6I0ex+wvKFMeLWEfx++He3zb3wtGZn48hoqEhVPZa+o6pHAdeHIw1A0sduu4rxv41nxb4VvNPmHYoXLO7SshzF1Zq9EaPZM3So1oE7b7iTl5e+zO6ju11enjdodiaOOIuLIlI+fUdEKgD+9+zKz0k+m8wzC56hWflm9I7pnfMFBoMf8lH7jwiSIAbNzcvo/8DEEWfxHPCziHwlIhOwLYb0f641KzBp166dy/J+ftHzHDt3zCMhPbLDlZq9FaPZc0RFRPG/5v9jxvYZ/PTnTy4ty1s0OwtH5lnMAeoBk4FJQKyqmj4LF3Dy5EmX5Lv+4Ho+W/sZAxoOoNY1tVxSRm5xlWZvxmj2LIOaDKJaiWoMnDOQ86nnXVaON2l2Bo60LADyA8nACaCGiDR3nUmBS3p8GWeSpmkM+HEAkYUiGdZymNPzzyuu0OztGM2eJTQ4lOG3Dmdn8k6XdnZ7k2ZnkGMgQRF5C+gObAXSrGTF9jjK4OV8ufFLViauJKFTAkULFPW0OQaDV9D2urbcecOdvLr8VXrW7kn5IuVzvijAcaRl0Rm4XlU7qOrt1naHi+0KSGJiYpya34nzJ3hmwTM0iWrCfTH3OTVvZ+Fszb6A0ewdvN/2fVTVZTO7vVFzXnDEWezCFh3W4GKqVHFujKZXl73KodOH+PjWjwkSR584uhdna/YFjGbvoELRCjxz4zN8u/Vblu9d7vT8vVFzXnDkF+QMsEFERjkjNpQha9LXKnAGfx75kw9XfUifOn2oXzbTCZlegTM1+wpGs/fw1I1PcW3EtTw+53Eupl10at7eqjm3OOIsZgKvACuwLVKUvhm8mCHzh5A/JD+vt3rd06YYDF5LWL4w3m7zNr/98xsJGxI8bY5Xk2MHt6p+kdM5BudQqpRzJsbP+2seM7fP5M1Wb1K6cGmn5OkqnKXZlzCavYvuNbszYvUInl30LN1qdKNIgSJOydebNeeGHAMJikhV4A2gBlAgPV1VK7vWtNzjq4EEnUFqWioxn8VwPvU8Wx/ZSv6Q/J42yWDwetYdWEeDMQ14ssmTvNP2HU+b4zHyFEgQGA+MBFKBm4EvAf9a1cNLSF+DOC+MXT+WbUnbeKfNOz7hKJyh2dcwmr2P2LKxxNWJ4+PVH7PrqHNiOnm75qvFEWdRUFUXYmuF7FXVYdjW4jY4mfQF3XPLifMneGHxCzSv0JzO1Ts7xygXk1fNvojR7J28esurhASFMHSBc9ZX8wXNV4MjzuK8iAQBf4rIABHpAhR2sV2GXPDG8jdIOpPEe23f86r4TwaDL1A2vCxPN32aKdum8Mvfv3jaHK/DkT6LBthWzSuKbVRUEeBtVV3lcutyia/2WaSlpREUlLv5EHuO7aH6iOrcXfNuvuzypZMtcx150eyrGM3ey+mU01QbUY2oiChWPrgyT/OTfEVzRvLUZ6Gqa1T1lKomqmofVb3Tmx2FLzNv3rxcX/vswmcREV675TUnWuR68qLZVzGavZdCoYV49eZXWb1/NZO3TM5TXr6i2VEcWSmvmoiMEZF5IrIofXOHcYHG33//navr1uxfwzdbvuHJJk9ybZFrnWyVa8mtZl/GaPZu7o+5nzql6/DsomfzFJXWlzQ7giNtpCnAeuB54KkMm8ELUFWeXvA0kWGRPH3j0542x2DweYKDgnm79dvsObaHT9d86mlzvAZHnEWqqo5U1dWqui59c7llAUiHDlc/yOynnT+xZM8SXmjxAhH5I1xglWvJjWZfx2j2ftpc14Y2ldvw6vJXOXbuWK7y8DXNOeGIs/hBRB4RkTIiUjx9c7llAUhSUtJVnX8x7SLPLHiG64pdR7/Yfi6yyrVcrWZ/wGj2Dd5q/RbJZ5N58+c3c3W9L2rODkecRW9sj50yxobK01AjESkqIlNF5A8R+V1EmlhOaL6I/Gm9FrPOFSt44U4R2SQi9fJStjezevXqqzr/y41fsuXQFt5o9QahwaEussq1XK1mf8Bo9g3qlqlLr9q9+OjXj9h3fN9VX++LmrPDkdFQlTLZ8hrq4yNgjqpWB2KwDc0dCixU1arAQmsf4FagqrX1wzabPOA5e+Es/1v8PxqWa0i3Gt08bY7B4Je8cvMrpGkaLyx5wdOmeByHBgGLSLSI3C0i96dvuS1QRIoAzYFxAKqaoqrHgE5AetDCL7AtuoSV/qXaWAUUFZEyuS3fm4mNjXX43E/WfML+k/t5q/VbPj0B72o0+wtGs+9QsWhFHm3wKF9u/JJtSduu6lpf1ZwVjiyr+iLQElsgwR+x/dP/GVuMqNxQCUgCxotIDLbHWo8D16jqQeucf4BrrPflgIxtwEQr7WCGNESkH7aWB6VLl2b06NEANGzYkMjISGbPng1A+fLladu2LWPHjgUgNDSUuLg4pk+fzqFDhwDo2rUrO3fuZOPGjQA0bdqU8PBw5s6dC0DlypVp3ry5PfZLWFgYvXr1YurUqSQnJwPQvXt3tmzZwtatWwFo0aIFISEhLFy4EIBq1arRoEEDJk6cCEBERAQ333wzkyZN4sSJEwD07NmTNWvWsGPHDgBatWpFamoqcxbPYdihYTQs0ZC6xeratRYvXpxu3boxYcIEzpw5A0BcXBzLli1j1y5bvJt27dpx8uRJ+/rAMTExVKlSxR57v1SpUnTu3JmEhAR7uIL4+HjmzZtnHwrYoUMHkpKS7M3s2NhYoqKimDFjBgBly5alY8eOjB071j4xKT4+nlmzZnHgwAEAOnXqRGJiIr/++ivr1q3zqXrq0aOHQ/W0dOlSAGrWrEl0dDSTJ0+22xEbG+tT9bRunW1MS27r6ejRo/bvqa/UU/r9VOWfKoQSSs9xPfl18K8O11Nqair79u3zqXrKFlXNdgM2Y2uBbLT2rwHm53RdNvnVxxaUsJG1/xG2meHHLjvvqPU6C7gpQ/pCoH52ZcTGxqovMmrUKIfOe37h88owdN2BdS62yPU4qtmfMJp9j2GLhynD0F8Tf3X4Gl/UDKzVLH5XHXkMdVZV04BUEYkADgF5mfmVCCSq6q/W/lSgHvBv+uMl6/WQdXz/ZeVFWWkByb+n/uWDVR9wd827qVfGb/v6DQavYnCTwZQMK8n/Lfw/T5viMRxxFmtFpCgwBtsjo/XAytwWqKr/APtE5HorqRWwDduKfL2ttN7ADOv9TOB+a1RUY+C4/ve4yq8oW7Zsjue8tvw1zqWe45WbX3GDRa7HEc3+htHse4TnD+e5Zs+xaPciFuxa4NA1vq75cnIMJHjJySIVgQhV3ZSnQkXqAGOBUGAX0Aeb4/oWKA/sBe5W1WSx9d6OANpjWw+8j6pmO3TXVwMJ5sSeY3uoNrwacXXiGH37aE+bYzAEFOdSz3H9iOspVagUq+NX+/TAkqzIUyBBEamXvgHFgRARuU5EcuwczwpV3aCq9VW1tqp2VtWjqnpEVVupalVVba2qyda5qqqPqup1qlorJ0fhy6R3PmXFK0tfIUiCeKGF/wzjy0mzP2I0+yYFQgrwYosXWXtgLTO3z8zxfH/QnBFHHkN9CqwCRmN7FLUSW7yo7SLS1oW2BRxpaWlZHttxZAdfbPyC/vX7ExUR5UarXEt2mv0Vo9l3uT/mfqoUr8L/Fv+PNM1ek79oTscRZ3EAqGu1BGKButgeHbUB3nalcYFGdrHvX1r6EvlD8jP0Jues4uUt+Fq8f2dgNPsuIUEhvNTyJTYf2syUrVOyPddfNKfjyOJHW1Q1OrM0EdmgqnVcaWBu8Lc+i62HtlJrZC2evvFp3myduzg1BoPBOVxMu0jMZzGkpqWy5ZEthATl+om815GnPgtgq4iMFJEW1vYpsE1E8gMXnGppgDNr1qxM019c8iKFQwvzVFP/iwyflWZ/xmj2bYKDgnn55pfZfmQ7X2/+Osvz/EkzOOYs4oCdwBPWtstKuwDc7BqzApP02ZgZ+e3gb0z7fRqDGg+iRFgJD1jlWjLT7O8Yzb5Pl+pdqFu6LsOWDOPCxcz/M/ubZkcCCZ5V1fdUtYu1vauqZ1Q1TVVPucPIQOalpS9RJH8RBjUZ5GlTDAaDhYjwUsuX2H1sN19t+srT5rgF/+qB8XE6dep0yf5vB39jxvYZDG4ymKIFinrGKBdzueZAwGj2DzpW60hsmVheXfZqpq0Lf9NsnIUXkZiYeMn+sKXDKFqgKAMbDfSQRa7ncs2BgNHsH4gIw1oOY/ex3Xy58cq4qv6m2WFnISJhrjTEgD1iJMD6g+uZuX0mgxoP8ttWBVyqOVAwmv2HDlU7UL9sfV5dfmXrwt80OzKDu6mIbAP+sPZjrBFRBhfy0tKXKFqgKI83etzTphgMhiwQEYa1GMaeY3sybV34E460LD4A2gFHAFR1I7bFiwxOpmHDhsB/rYrBjQdTpEARD1vlWtI1BxJGs39xW9XbaFC2wRWtC3/T7NBjKFW9fAHaiy6wJeCJjIwE4JVlr1AkfxG/7qtIJ11zIGE0+xciwostXmTPsT1M2DTBnu5vmh1xFvtEpCmgIpJPRIZgWzPb4GRmz57Npn83Mf2P6Tze6HG/b1UA9pW8Agmj2f+4rept1CtTj9d/fp3UtFTA/zQ74iz6A49iW8p0P1DH2je4gNeWv0Z4aDiPNzZ9FQaDryAiPN/seXYm72TylsmeNsclODIp77Cq9lTVa1S1lKr2UtUj7jAu4IiEKVunMKDhAIoXLO5pa9xC+fLlPW2C2zGa/ZNO1TsRXSqa15a/xsW0i36nOcsIWCIyHMgyyqCq+v8DdTezTJdRMF9BBjUOnNnabdsGXpR7o9k/CZIgnm/2PD2m9WDa79Po1rabp01yKtm1LNZiW0a1ALY1sv+0tjrYVrgzOJGdyTv5evPXPFz/YSIL+VfHWHb42wIxjmA0+y/danTj+hLX8+qyVxk9xr9Ws8yyZaGqXwCIyMPATaqaau1/Bix3j3mBw9u/vE0wwQxpOsTTphgMhlwSHBTMc82e4/7p97O52GZPm+NUHOngLgZEZNgvbKUZnMT+E/tJ2JBA88LNKV24tKfNcSuhoYHXSDWa/Zt7at1DxaIVmXN6DjmtF+RLOOIs3gR+E5EEEfkCWA+87lqzAov3Vr5HmqYx7sFxnjbF7cTFxXnaBLdjNPs3IUEhPN30aXal7GLJniWeNsdpODIaajzQCPge+A5okv6IypB3Dp85zKh1o+hZuycblmzwtDluZ/r06Z42we0Yzf5Pn7p9KBpSlNd/9p//1Y7O4P5HVWdY2z+uNiqQ+PjXjzl74SxDbxzKoUOHPG2O2zGaA4NA01wgpAC3FLyFBbsWsHr/ak+b4xRMiHIPcuL8CYavHk6XG7pwQ+QNnjbHYDA4kRZhLShaoChv/PyGp01xCh5zFiISLCK/icgsa7+SiPwqIjtFZLKIhFrp+a39ndbxip6y2dmMWjuKY+eO8X83/R8AXbt29bBF7sdoDgwCUXPPu3oysOFApv8xna2HtnranDyTpbMQkeLZbU4o+3EujTH1FvCBqlYBjgIPWukPAket9A+s83ye86nn+WDVB7Su3Jr6ZesDsHPnTg9b5X6M5sAgUDU/1ugxCoYU5J0V73janDyTXctiHf9NzEsCdmCblJdkpeUaEYkCOgBjrX0BbgGmWqd8AXS23ney9rGOt7LO92m+2vQVB08d5OmmT9vTNm7c6EGLPIPRHBgEquaSYSV5sO6DTNw8kcQTvr1yXnaT8ioBiMgY4HtV/dHav5X/fshzy4fA00C4tV8COJY+8Q9IxBa4EOt1n2VTqogct84/nDFDEekH9AMoXbo0o0fbZk82bNiQyMhIewTI8uXL07ZtW/uM0tDQUOLi4pg+fbq9E65r167s3LnT/gVv2rQp4eHhzJ07F4DKlSvTvHlzEhISAAgLC6NXr15MnTqV5ORkALp3786WLVvYutXW/GzRogUhISEsXLiQNE3j9eOvE1Mqhl0LdjF64WgiImxTWSZNmsSJEycA6NmzJ2vWrGHHjh0AtGrVitTUVJYuXQpAzZo1iY6OZvJkW+Cy4sWL061bNyZMmMCZM2cA25DFZcuWsWvXLgDatWvHyZMnWbFiBQAxMTFUqVKFadOmAVCqVCk6d+5MQkICKSkpAMTHxzNv3jz+/vtvADp06EBSUhKrV9s67mJjY4mKimLGjBkAlC1blo4dOzJ27FjS0tIICgoiPj6eWbNmceDAAcC2PnFiYiKHDx9m9OjRXllPANWqVaNBgwZMnDgRgIiICHr06JGnejp69CiAT9VT+qpvua2n06dP2+9JX6mnvN5Phw8fZvr06TzZ8kk+XfMpfUb34a6Iu7y6nrJFVbPdgM2OpDm6AR2BT633LYFZQElgZ4ZzrgW2WO+3AFEZjv0FlMyujNjYWPVmpm2bpgxDJ22edEn65s2bPWSR5zCaA4NA13zvtHu18OuFNflMsgctyhlgrWbxu+pIB/cBEXleRCpa23PAAQeuy4obgTtEZA8wCdvjp4+AoiKS3tKJwhYOHev1WgDreBGsVft8EVXlrV/eonKxynStcaknDw8Pz+Iq/8VoDgwCXfPTTZ/mVMopPl3juytSO+Is7gEisU3K+x4oZaXlClX9P1WNUtWKQA9gkar2BBYD6WEaewMzrPczrX2s44ssD+iTLN27lNX7VzOkyRBCgi59CpjeLA8kjObAINA1x5SOoX2V9nz060ecvXDWg1blHkdmcCer6uOqWtfaHlfVZBfY8gwwWER2YuuTSI99MQ4oYaUPBoa6oGy38c6Kd4gMiySuTpynTTEYDG7kmRufIelMEl9u/NLTpuSKLDu40xGRSGyd0TWxhSsHQFVvyWvhqroEWGK93wVcscK5qp4D7sprWd7A1kNb+fHPH3m55csUzFfwiuOVK1f2gFWexWgODIxmaFGhBfXL1ue9le/RN7YvQeJbc6IdsXYi8AdQCXgJ2AOscaFNfsv7K9+nYEhBHm7wcKbHmzdv7maLPI/RHBgYzbalV4c0GcKfyX/yw/YfPGRV7nHEWZRQ1XHABVVdqqoPYOuUNlwFB08eZMLmCfSp04eSYSUzPSd96GAgYTQHBkazja41ulKhSAXeXfmu+w3KI444iwvW60ER6SAidYHAWCDaiYxYPYILFy8wqEngLJlqMBguJSQohEGNB/Hz3z+zKnGVp825KhxxFq+KSBHgSWAItlnX5hfvKjiVcoqRa0fS5YYuVCleJcvzwsLC3GiVd2A0BwZG8388WO9BihYoynsr33OzRXlDfHgUapbUr19f165d62kz7Az/dTgD5wxkxQMraHJtE0+bYzAYPMyzC5/lrV/eYseAHVxX/DpPm2NHRNapav3MjmUXSHC4iHyc1eY6c/2Li2kX+WDVBzSJapKjo5g6dWq2x/0RozkwMJov5bGGjxEswXz060dutChvZPcYKj2IYAGgHrYggn8CdYDAWVA3j8zcPpPdx3YzuMngHM9Nj4MTSBjNgYHRfCllwstwT617+Py3zzl27pj7jMoDWToLVf1Cbcun1gZaqupwVR0OtMLmMAwO8P6q96lYtCKdq3f2tCkGg8GLGNR4EKcvnGbMujGeNsUhHOngLgZEZNgvbKUZcmDN/jX8/PfPDGw48IrQHpnRvXt3N1jlXRjNgYHRfCV1Stfh5oo3M3z1cC5cvJDtud6AI87iTeA3EUkQkS+A9YD/rELuQj5Y9QHhoeE8WO/BnE8GtmzZ4mKLvA+jOTAwmjNnUONB7Duxj2m/T3ODRXnDkdhQ44FG2IIIfgc0sR5PGbJh3/F9TNk2hfh68UTkj8j5ArDH6g8kjObAwGjOnA7VOlC1eFXeX/k+3j4yNbvRUNWt13pAWWwLEO0DylpphmwYsXoEaZrGwEYDPW2KwWDwUoIkiCcaP8GaA2tYsW+Fp83JluxaFunDd97LZPO9uepu5HTKacasH0OX6l2oWLSiw9e1aNHCdUZ5KUZzYGA0Z03vmN4ULVDU64fRZresaj/r7a1W5Fc7IlIgk0sMFhM2TeDouaM83ujxq7ouJCTnTnB/w2gODIzmrCkUWoj4uvF8sOoD9h3fx7VFrnWxZbnDETUrsM2zyCnNgG0lvI9Xf0zd0nW5qfxNV3XtwoULue46183mvHDhAomJiZw7dy7nk93EyZMn7WtIBwpGs2cpUKAAUVFR5MuXz6XlXM39PKDhAN5f9T6frvmUN1q/4VK7ckuWzkJESgPlgIJW8ECxDkUAgRfoxUEW7l7ItqRtJHRKQERyvsCNJCYmEh4eTsWKFb3GtqSkJCIjIz1thlsxmj2HqnLkyBESExOpVKmSp82xU6FoBTpX78zo9aP5X4v/EZbP+35is+uzaIetbyIKeJ//+isGA8+63jTf5KNfP6JUoVL0iO5x1ddWq1bNBRb9x7lz5yhRooTXOAqw/csLNIxmzyEilChRwi2t66u9nx9v9DjJZ5OZuGmiiyzKGznN4L4ZiFPVmzNsd6jqd2600WfYmbyT2Ttm81DsQ+QPyX/V1zdo0MAFVl2KNzkKMNFIAwVv0uyue+Bq7+dm5ZsRc00MH/36kVcOo3VkUt4sEblXRJ4VkRfSN5db5oOMWD2CkKAQHq6f+Up4OTFxonf+o3AlJmZQYBCImq/2fhYRHm/0OFuTtrJo9yIXWZV7HHEWM4BOQCpwOsNmyMDJ8ycZv2E8d9W8izLhZTxtjlfz77//cu+991K5cmVat25NkyZN+P777z1qU3x8PNu2bfOoDQbDPbXuoWRYSUasGeFpU67AkdFQUara3uWW+DhfbfqKE+dP8FjDx3KdR0SEYzO9fRlVpXPnzvTu3Zuvv/6a5ORkTp48ycyZMz1q19ixY91WVnBwsNvK8hYCUXNu7ucCIQXoW68vb/3yFnuP7aVC0QousCx35Lj4kYiMBoar6mb3mJR33L34kapS89OaFAotxOr41V7XL5DO77//zg033ADAE3OeYMM/G5yaf53Sdfiw/YfZnrNw4UJefvllli5desWxPXv2cN9993H6tK3hOmLECJo2bcqSJUsYNmwYJUuWZMuWLcTGxjJhwgREhJdffpkffviBs2fP0rRpU0aNGoWI0LJlSxo1asTixYs5duwY48aNo1mzZly8eJFnnnmGOXPmEBQURN++fXnsscdo2bIl7777LvXr1+fhhx9mzZo1nD17lm7duvHSSy8BMHToUGbOnElISAht27bl3XfN3FRfJeO94G3sO76Pih9V5KmmT/Fm6zfdWnauFj/KwE3AOhHZLiKbRGSziGzKgzHXishiEdkmIltF5HErvbiIzBeRP63XYla6WAsu7bTK97r5HYt2L+L3w78zoMGAPDmKSZMmOdEq72Tr1q3Uq/dfFWZ8ll2qVCnmz5/P+vXrmTx5MgMH/hcq5bfffuPDDz9k27Zt7Nq1i19++QWAAQMGsGbNGrZs2cLZs2eZNWuW/ZrU1FRWr17Nhx9+aP/BHz16NHv27GHDhg1s2rSJnj17XmHja6+9xtq1a9m0aRNLly5l06ZNHDlyhO+//56tW7eyadMmnn/++Vx/BoH4/D4QNef2fr62yLV0rt6ZMevHcPbCWSdblXsceQx1q5PLTAWeVNX1IhKOzRHNB+KAhar6pogMBYYCz1jlV7W2RsBI69VrGLFmBCXDStI9Om9hmE+cOOEki3ImpxaAuxgyZAjr1q0jNDSUBQsWMGDAADZs2EBwcDA7duywn9ewYUOioqIAqFOnDnv27OGmm25i8eLFvP3225w5c4bk5GRq1qzJ7bffDsCdd94JQGxsLHv27AFgwYIF9O/f3z67tnjx4lfY9O233zJ69GhSU1M5ePAg27Zto0aNGhQoUIAHH3yQjh070rFjx1xrvnjxYq6v9VUCUXNe7ucBDQbw3e/fMWnLJPrU7eNEq3KPI1Fn96rqXuAsoBm2XKGqB1V1vfX+JPA7tsl/nYD0aLZfAJ2t952AL9XGKqCoiHhND/LeY3uZuX0mfev1pUCId4wl92Zq1qzJ+vXr7ftvvfUWCxcuJCkpiQ8++IBrrrmGjRs3snbt2ktm/ObP/99Q5ODgYFJTUzl37hyPPPIIU6dOZfPmzfTt2/eS8fPp16Sf7wi7d+/m3XffZeHChWzatIkOHTpw7tw5QkJCWL16Nd26dWPWrFm0b2+68Qyuo2XFltSMrMnw1cO9Zhhtji0LEbkD22S8ssAhoAK2H/iaeS1cRCoCdYFfgWtU9aB16B/gGut9OWzRbtNJtNIOZkhDRPoB/QBKly7N6NGjAds/0sjISGbPng1A+fLladu2rb1DMzQ0lLi4OKZPn86hQ4cA6Nq1Kzt37mTjxo0ANG3alPDwcObOnQtA5cqVad68OQkJCXx34jtUlf71+zN16lR7c7t79+5s2bLFHqa4RYsWhISEsHDhQsA2YadBgwb24XURERH07NmTSZMm2f+R9OzZkzVr1tj/Ybdq1YrU1FT78/6aNWsSHR3N5MmTAdu/5G7dujFhwgTOnDkDQFxcHMuWLWPXrl3UqVOH8+fPk5aWxqlTpwAoWLAgBQoU4OjRo4Atnk2xYsU4fPiw/UtasmRJTpw4Yf/xLlKkCKmpqfa+hbCwMEJDQzl27BgA+fLlo2jRoiQlJdnrJzIykmPHjlGrVi1OnTrFiBEj6NOnD6pKYmIiqkpycjIlSpTgyJEjfPvtt1y8eJGkpCSOHTtmL/vo0aOcPXuWkydPcurUKVQVVWX37t1MmTKFLl26kJSUxIULFzh16hRpaWkcPnyYtLQ0jhw5Qps2bRg+fDjR0dGEhISgqoSFhXHhwgWOHj1KWloaYWFhpKSksHXrVn788UeaN2/O7t27OXv2LI0bN+bGG2+kUqVKdn3FixfnzJkzdkcVHh4O2EJcZPYZp3f2HjlyhLS0NABKlCjBqVOnOH/+vP374Ml6unDBthhP0aJFSUlJsX+fChUqREhICMePH7ffPxERERw+fBiwDf8sWbIkR48etTvoYsWKUaBAAXs5hQsXJigoyP49z58/P4ULF+bIkSMABAUFUaJECZKTk+0tkmLFinHu3DnOnj2b6WdcoEABwsLC7PdfcHAwxYsXvySPjPV08uRJ/vrrrzzdTwDt2rXj5MmTrFhhixgbExNDlSpVmDZtGmlpaUyfPp3OnTuTkJBgr5f4+HjmzZvH33//DUCHDh1ISkpi9erVgK0lHBUVRcz5GL4+8TXvTn6Xp3o8xdixY0lLSyMoKIj4+HhmzZrFgQMHAOjUqROJiYmsW7cOyP3vXrak32xZbcBGoATwm7V/MzAup+scyLcwtjW+77T2j112/Kj1Ogu4KUP6QqB+dnnHxsaqOzh74ayWeKuEdpnUxSn5LV682Cn5ZMW2bdtcmr+jHDhwQLt3764VK1bUevXqacuWLXXSpEm6Y8cOrVWrltauXVuffvppLVSokKraPpcOHTrYr3/00Ud1/Pjxqqr63HPPaeXKlbVp06YaFxenL774oqqqtmjRQtesWaOqqklJSVqhQgVVVb1w4YIOGjRIb7jhBq1du7YOHz78ivN79+6tVatW1VtuuUW7dOmi48eP1wMHDmiDBg20Vq1aGh0drQkJCbnWf+LEiVxf66t4m2Z33At5vZ9Pnj+pRd4oovdOu9c5BjkAsFaz+s3O6oD+9+O8Vv9zGkHp73O6Loc88wFzgcEZ0rYDZaz3ZYDt1vtRwD2ZnZfV5i5n8eWGL5Vh6IK/Fjglv1GjRjkln6zwFmeRkUOHDnnaBLdjNHsed9wLzrifB/44UPO9nE//PfWvEyzKmeychSOjoY6JSGFgGTBRRD4iD5PyxDZcaBzwu6q+n+HQTKC39b43tsmA6en3W6OiGgPH9b/HVR7l07Wfcn2J67ml0i2eNsVgMPghDzd4mAtpFxi3fpynTXHIWXQCzgCDgDnAX8DteSjzRuA+4BYR2WBtt2Fb67uNiPwJtLb2AX4EdgE7gTHAI3ko22msP7ieVYmreLj+w06bV9GqVSun5ONLpD97DiSM5sDAGfdz9ZLVuaXSLXy27jMupnl2RFl2IcqrYOt0/sVKSgO+EJGbgKLAkdwUqKo/81+488u54tO1mkaP5qYsVzJyzUgKhhSkd53eOZ/sII6O2DEYDN6Ps+7nR+o/Qrcp3fjxzx+5/fq8/E/PG9m1LD4EMhsofNw6FrAcO3eMr7d8Tc9aPSlaoKjT8s1sVrO/kz6aJZAwmgMDZ93Pd1x/B2XDy/Lp2k+dkl9uyc5ZXKOZhPiw0iq6zCIf4MuNX3LmwhkebpC76LIGA9hms//www+eNsPg5eQLzke/ev2Ys3MOfyX/5TE7snMWRbM5VtDJdvgMqsrItSNpVK4R9co4N/JIzZp5nrri9WSMOBsbG0uHDh08HnEW3Bt1tmDBgqSmpvLkk09eEvokK7whIq6qcsstt9jnRjzwwAOUKlWK6OjoS85LTk6mTZs2VK1alTZt2tjnhRQs+N9PxpEjR7j55pspXLgwAwYMsKefOXOGDh06UL16dWrWrMnQoUPtxxISEoiMjKROnTrUqVPnksCPX3zxBVWrVqVq1ap88cUX9vTWrVvby/cEzryf+8b2JSQohJFrRzotz6smq2FSwDdA30zS44HJWV3nDZsrh84u3r1YGYZ+seELp+d97Ngxp+eZEU8PnU1LS9PGjRvryJEj7Wk7d+7Ujz/+2INWuZ8LFy7otm3bdNWqVZ42xWFmzZqlTzzxhH1/6dKlum7dOq1Zs+Yl5z311FP6xhtvqKrqG2+8oU8//bSq2jSnc+rUKV2+fLmOHDlSH330UXv66dOnddGiRaqqev78eb3pppv0xx9/VFXV8ePHX3JuOkeOHNFKlSrpkSNHNDk5WStVqqTJycmqqpqQkKCvvvpqpnrccS84+37uOrmrlnirhJ69cNap+WaEXA6dfQLoIyJLROQ9a1sKPAg87loX5r18tvYzihUoxl017nJ63ukzR72JlSvhjTdsr3ll0aJFhIaG0r9/f3taREQEjz1mC+u+Z88emjVrRr169ahXr559VuySJUto2bIl3bp1o3r16vTs2TP9jwsvv/wyDRo0IDo6mn79+tnTW7ZsyTPPPEPDhg2pVq0ay5cvB2wxioYMGUJ0dDS1a9dm+PDh9vPTIxU//PDD1K9fn5o1a/Liiy/abR06dCg1atSgdu3aDBky5Ap9w4YNo3fv3jRr1owKFSrw3Xff8fTTT1OrVi3at29vnxX93HPPcf/99/Pggw/abU5NTaVBgwYsWbIEgP/7v//jueeeu8K2woUL89RTT1GzZk1at27N6tWradmyJZUrV7aHec/qczx48CDNmzenTp06REdH2z+TdObMmcNdd/33vV6yZIk9BtbEiRPp1KmT/Vjz5s0zjas1Y8YMeve2Dfro3bs306dPB7jkH36hQoW46aabrlhqNSwsjJtvvhmwzTCuV68eiYmJV5SRkblz59KmTRuKFy9OsWLFaNOmDXPmzAHgjjvu4Jtvvsn2elfi7Pu5f/3+HDl7hGnbpjk1X4fJyoukb9hmbD9mbbfkdL43bK5qWfxz8h/N93I+HTRnkEvy97ZJeStWqBYsqBocbHtdsSJv5X/00UeX/DtVvXSy1unTp/XsWdu/ph07dmh6PS5evFgjIiJ03759evHiRW3cuLEuX75cVW3/LNPp1auXzpw5U1VtM7IHDx6sqqqzZ8/WVq1aqarqp59+ql27drX/002/PuMM7vS01NRUbdGihW7cuFEPHz6s1apV07S0NFVVPXr06BX6XnzxRb3xxhs1JSVFN2zYoAULFrT/M+7cubN+//33qqq6fft2VbW1tO655x67zVu2bNHq1avr/PnztU6dOnr+/PkrbAMuybNNmzb28mJiYrL9HN999137P+3U1NQrZlVfuHBBr732Wj116pSqqvbv31+/+uorVVUtX778Fefv3r37ipZFkSJF7O/T0tLs+5lNysuqtaBq+3wrVaqkf/31l/3c0qVLa61atbRr1676999/q6rqO++8o6+88or9updfflnfeecd+36VKlX08OHDV+TvK5PyMnIx7aJW+biKNvu8mVPzzQh5mZSnqotVdbi1ed9af25k/IbxXEi7wEOxD7kk/8z+qXmSJUsgJQUuXrS9Wn96ncajjz7KzTffbF+r+MKFC/Tt25datWpx1113XfKcPj3qbFBQkD3qLMDixYtp1KgRtWrVYtGiRfZYXJB11NmHHnoox6iz9erVo27dumzdupVt27ZRpEgRe9TZ7777Lss1pW+99Vby5ctHrVq1uHjxoj3gYK1atew2rF69mptvvpnmzZvz66+/2m2uWbMm9913Hx07duTzzz8nNDT0ivxDQ0MvybNFixb28tLzz+pzbNCgAePHj2fYsGFs3rz5irkPISEhtG/fnh9++IHU1FRmz55tb00kJydf9VwJEbHPQbqaxY9SU1O55557GDhwIJUrVwbg9ttvZ8+ePWzatIk2bdrYWy85UapUKXv8JHfj7Ps5SIJ4KPYhlv+9nK2HtuZ8gZNxZFKeAUjTNEavG03Lii25vuT1LimjW7duLsk3t7RsCaGhEBxse23ZMm/5XR5x9pNPPmHJkiX2AHP+EHU2vcygoCDy5ctn/7EMCgoiNTWV8+fPM2TIEL755huWL19Or169LrF58+bNFC1a1B7c7XIuzzNjeekas/ocmzdvzrJlyyhXrhxxcXF8+eWXV+Tfo0cPvv32WxYtWkT9+vXtDiIkJMQe9DA7rrnmGg4etAVYOHjwIKVKlQKu7oezX79+VK1alSeeeMKeVqJECbvW+Ph4e8C8cuXKsW/ff3FGExMTKVeunH3/3Llzl3SuuxNX3M9xdeIIDQ5l1LpRTs87J4yzcJD5f81n97Hd9I/tn/PJuWTChAkuyzs3NGkCCxfCK6/YXps0yVt+t9xyC+fOnWPkyP9GdOzfv9/+/vjx45QpU4agoCC++uqrHNdASP+RLVmyJKdOnWLq1Kk52tCmTRtGjRpl/2G9fFGeEydOUKhQIYoUKcK///7LTz/9BMCpU6c4fvw4t912Gx988IE9IvHVcvbsWS5evEiRIkU4deoU06b99/z5u+++Izk5mWXLlvHYY4/Zo8NeLVl9jnv37uWaa66hb9++xMfHX+K402nRogXr169nzJgx9OjRw55+/fXX2yOtZscdd9xhH5H0xRdf2Fsm8+fP5/7778/x+ueff57jx4/z4YcfXpKe7oAAZs6caV/lrl27dsybN4+jR49y9OhR5s2bR7t27QDbI/Z//vmHihUr5liuK3DF/VwyrCTdanSzD993J8ZZOMhn6z4jMiySLjd0cVkZ6WGQvYkmTeD//i/vjgJsjyWmT5/O0qVLqVSpEg0bNuTRRx/lrbfeAuCRRx7hiy++ICYmhj/++INChQplm1/RokXp27cv0dHRtGvXzv44Kzvi4+MpX748tWvXJiYmhq+//vqS4zExMdStW5fq1atz7733cuONNwK2SWUdO3akdu3a3HTTTbz//vuZZZ8jRYsW5d57773C5sOHDzN06FDGjh1LtWrVGDBgAI8/nrtxJFl9jkuWLLHrmzx5cqb5BwcH07FjR3766adLFnjq0KGDvfMd4J577qFJkyZs376dqKgoxo2zxS4aOnQo8+fPp2rVqixYsMA+/HXfvn2X/MOvWLEigwcPJiEhgaioKLZt20ZiYiKvvfYa27Zto169epcMkf3444+pWbMmMTExfPzxxyQkJAC2Fsv//vc/GjRoQIMGDXjhhRfsrZh169bRuHFj+yNHd+Oq+7l/bH+Onz/OpC1uXlkzq84MX96c3cGdeDxRg18K1mfmP+PUfC/H2zq43YG3RSN1B76o+cCBA9q6detcX//II4/oxo0bnWhRzgwcOFAXLMg8IrQvdnCnk5aWpjU+qaGNxjRyet7kMepswDN+w3gu6kX61uvr0nLi4uJcmr83UqJECU+b4HZ8UXOZMmXo27dvrpcKHT58OLVr13ayVdkTHR3t0eCcrrqfRYS+9fry6/5f2fTvJpeUkRnGWeRAmqYxdv1YWlVqxXXFr3NpWcuWLXNp/t5I+kpwgYSvar777ruJiIjI1bWe0Ny3r2v/3OWEK+/n+2rfR/7g/IxZN8ZlZVyOcRY5MP+v+ew9vtflrQrAoQ5EfyN9GdFAwmgODFx5P5cIK0HXGl35atNXbuvoNs4iB0avH03JsJJ0rt7Z06YYDAaDnX71+nH8/HGmbJ3ilvKMs8iGf079w8ztM4mLiSN/SP6cL8gj6UP+AoncPtbwZYzmwMDV93PzCs2pVqIaY9a751GUcRbZkLAhgdS0VOLrxbulvECM+e/IRC9/w2gODFx9P6d3dP+y7xe3zOg2ziIL0jSNMevH0KJCC5fN2L6c9IBvgUR6x+eSJUsCRr+vdnDnhUDU7I7vc++Y3uQLyueW1oVxFlmwZM8Sdh3d5bZWRaBQuHDhK9IOHDjAa6+9Rt26dR3Op2nTpoAtwurlE+sMhkAhspBtovBXm77ifKprBxEYZ5EF434bR5H8Reh6Q1e3lRkTE+O2sryFggULsnnzZsaNG3dVMXzS/7X5orPwVKwiTxKImt11Pz9Y90GSzyYz/Y/pLi3HM/PgvZyjZ48ybds04uvFUzCf+77kVapUcVtZAN1HXblIRcfaZbivSUXOplwkbvzqK453i43irvrXknw6hYcnrLvk2OSHrj4mSIECBVi5ciWbN29myJAhtGzZkrp167J8+XJOnz7Nl19+yRtvvMHmzZvp3r07r776KmBroZw6dYqhQ4fy+++/U6dOHXr37s3AgQMZOnQoS5Ys4fz58zz66KM89JBrogTnlsvXcQgEAlGzu+7n1pVbU6FIBcb+Npbu0d1dVo5pWWTCxM0TOX/xvNsfQWUMKhcoZLbsZWhoKGvXrqV///506tSJTz75hC1btpCQkMCRI0cuOffNN9+kWbNmbNiwgUGDBjFu3DiKFCnCmjVrWLNmDWPGjGH37t3ukuMQnlzq01MEomZ33c9BEsQDdR9gwa4F7D7quu+6aVlchqoydv1Y6pWpR53SdTxtjkvJriVQMDQ42+PFC4XmqiXhCHfccQdgW6+hZs2alClTBoDKlSuzb9++bMNlzJs3j02bNtkj0B4/fpw///yTSpUqucRWg8EbiKsTx7Alwxi/YTwv3/yyS8rwmZaFiLQXke0islNEhuZ8Re5Yf3A9G//dSHxd93dsp8f+DyQyiwiacY2GjOtYZFyzIStUleHDh7NhwwY2bNjA7t27adu2rXONziOeioLqSQJRszvv5/JFytOuSjtbHLu07EP75xafcBYiEgx8AtwK1ADuEZEarihr3G/jKBhSkHtq3eOK7LOlc+fObi/T0xQrVixP14eHh18ynr1du3aMHDnSvt71jh07OH36dJ7KcDZ51eyLBKJmd9/P8XXjSTyRyLy/5rkkf59wFkBDYKeq7lLVFGAS0CmHa66aMxfOMHHzRLrV6EbRAkWdnX2OpMfo92fOnDlDVFSUfXvllVfylF/t2rUJDg4mJiaGDz74gPj4eGrUqEG9evWIjo7moYcecniVPHdx+PBhT5vgdgJRs7vv59uvv53IsEjG/jbWJfmLLYS5dyMi3YD2qhpv7d8HNFLVARnO6Qf0AyhdunTsSy+9BNjWbo6MjGT27NkAlC9fnrZt29oXVQkNDSUuLo7p06fz58E/mXJiCi/e9iIlz5S0r4bWtGlTwsPDmTt3LmB7dt68eXP7lyEsLIxevXoxdepU+8pr3bt3Z8uWLfb1lVu0aEFISAgLFy4EoFq1ajRo0ICJEycCtnAIJ06csL8C9OzZkzVr1rBjxw4AWrVqRWpqKkuXLgVsy5RGR0czefJkwLYQTLdu3ZgwYYJ94ZW4uDiWLVvGrl27qFOnDjExMaSlpdknSRUsWJACBQrYOyBDQkIoVqwYhw8fJv27UbJkSU6cOGFfnrNIkSKkpqba/7GHhYURGhpqX9ktX758FC1a1L5cKkBkZCTHjh2z/+MvWrQoKSkpnDhxgpCQEAoVKkRISAjHjx+310tERIT9R0ZEKFmyJEePHrX/+BcrVoxz585x9uxZwDZCKigoyP755c+fn8KFC9s7xYOCgihRogTJycn21eMuzyN9GdH01kqBAgUICwuz12twcDDFixe/JI/ixYtz5swZ+8p9l+dx+WecmppKmTJlOHLkiH1mc4kSJTh16pQ94F5ERIRX1VP69ym39XTkyBGCgoK8pp52795NiRIl8nQ/ga0le/LkSftQ7piYGKpUqcK0adM4fPgwNWrUoHPnziQkJNjrJT4+nnnz5vH3338DtoWlkpKSWL3aNvowNjaWqKgoZsyYAUDZsmXp2LEjY8eOJS0tjaCgIOLj45k1a5Z9ffFOnTqRmJjIK0tfIUVTeO2W1yhVqpRDv3vpS/h27dqVkiVLrlPV+mSC3ziLjNSvX1/Xrl3rThOdwujRo+nXr5/L8v/999/ty1F6C0lJSURGRnraDLdiNHsed9wLrr6fXYGIZOksfOUx1H7g2gz7UVaaXxEfH3izxUuWLOlpE9yO0RwY+Nv97CvOYg1QVUQqiUgo0AOY6WGbnM68ea7pmMqIt7Ukc7vymi9jNHsWd90D7rif3YlPOAtVTQUGAHOB34FvVdX1YRbdTPozTFdRoEABjhw54lUOI/05biBhNHsOVeXIkSNumVHu6vvZ3fjM4GdV/RH40dN2+DJRUVEkJiZe0qHpaU6ePBlwI2WMZs9SoEABoqKiPG2Gz+EzziIQ6NChg0vzz5cvn9fNZN6/fz/lypXztBluxWgODFx9P7sbn3gMFSh40z9+d2E0BwZGs+9jnIUXkT7OOpAwmgMDo9n3Mc7CYDAYDDniE5PyrhYRSQL2etqOXFAS8I5eQPdhNAcGRrNvUEFVM5096ZfOwlcRkbVZzZ70V4zmwMBo9n3MYyiDwWAw5IhxFgaDwWDIEeMsvIvRnjbAAxjNgYHR7OOYPguDwWAw5IhpWRgMBoMhR4yzMBgMBkOOGGfhJYhIURGZKiJ/iMjvItLE0za5EhEZJCJbRWSLiHwjIq4PA+oBRORzETkkIlsypBUXkfki8qf16jcLVGeh9x3re71JRL4XkaIeNNHpZKY5w7EnRURFxOcX9DDOwnv4CJijqtWBGGyh2P0SESkHDATqq2o0EIxtjRJ/JAFof1naUGChqlYFFlr7/kICV+qdD0Sram1gB/B/7jbKxSRwpWZE5FqgLeAXscqNs/ACRKQI0BwYB6CqKap6zKNGuZ4QoKCIhABhwAEP2+MSVHUZkHxZcifgC+v9F0Bnd9rkSjLTq6rzrDVpAFZhW+nSb8iijgE+AJ4G/GIUkXEW3kElIAkYLyK/ichYESnkaaNcharuB97F9o/rIHBcVf1rWbHsuUZVD1rv/wGu8aQxbuYB4CdPG+FqRKQTsF9VN3raFmdhnIV3EALUA0aqal3gNP71aOISrGf0nbA5ybJAIRHp5VmrPIPaxq77xT/PnBCR54BUYKKnbXElIhIGPAu84GlbnIlxFt5BIpCoqr9a+1OxOQ9/pTWwW1WTVPUC8B3Q1MM2uZN/RaQMgPV6yMP2uBwRiQM6Aj3V/yd3XYftj9BGEdmD7bHbehEp7VGr8ohxFl6Aqv4D7BOR662kVsA2D5rkav4GGotImIgINr1+26GfCTOB3tb73sAMD9rickSkPbZn93eo6hlP2+NqVHWzqpZS1YqqWhHbn8F61n3usxhn4T08BkwUkU1AHeB1z5rjOqwW1FRgPbAZ2/fQr0IjpCMi3wArgetFJFFEHgTeBNqIyJ/YWllvetJGZ5KF3hFAODBfRDaIyGceNdLJZKHZ7zDhPgwGg8GQI6ZlYTAYDIYcMc7CYDAYDDlinIXBYDAYcsQ4C4PBYDDkiHEWBoPBYMgR4ywMfomIXLSGaW4RkSnWrNq85vmyiLS+yms+FJHm1vslIrLdir76h4iMcCQCq4icyqXJjto4SUSqurIMg+9jnIXBXzmrqnWsqLYpQP+MB60AhleFqr6gqgscPV9ESgCNrUBz6fS0oq/WBs7j5Al5YuNq7+uR2CbNGQxZYpyFIRBYDlQRkZYislxEZgLbRCTYWmthjfVv/6H0C0TkGRHZLCIbReRNKy1BRLpZ71tZQR83W+sZ5M+k3K7AnMwMUtUUbD/Q5UUkxspzsNUS2iIiT1x+jYgUFpGFIrLeKreTlV7RarF8CWwBrhWRpzLoesk6r5CIzLY0bRGR7hk+n9a5caCGwMF8OQx+jfUDeCv//WjXw7a2wm4R6Yct4m0D68f+FxGZB1THFuiwkaqeEZHil+VZANsaBq1UdYf1I/0w8OFlxd+IbaZ6pqjqRRHZCFS37OwDNAIE+FVElqrqbxkuOQd0UdUT1mI6qyzHB1AV6K2qq0SkrbXf0MprpvUoLBI4oKodLB1FLDvSRGQntnVU1uXwkRoCFNOyMPgrBUVkA7AWWyyqcVb6alXdbb1vC9xvnfcrUALbj2xrYHx6HCNVvXytguuxBULcYe1/gW09ksspgy30fHaI9XoT8L2qnlbVU9iCKzbL5NzXrZAwC4By/BfefK+qrsqgqy3wG7aQKtUtXZuxhRl5S0SaqerxDHkfwhYB2GDIFNOyMPgrZ1W1TsYEW8xCTmdMAh5T1bmXndfOWTYAWS4XKyLBQC1sQRQdiUjaE1vrIFZVL1gRTdPzv1zXG6o6KpMy6wG3Aa+KyEJVfdk6VMCy12DIFNOyMAQyc4GHRSQfgIhUsxadmg/0SR9BdfljKGA7UFFEqlj79wFLM8n/d6BKJulYZb4B7FPVTdj6DTpbkXgLAV2stIwUAQ5ZjuJmoEI2uh4QkcJWWeVEpJSIlAXOqOoE4B0uDYNfDVt/h8GQKaZlYQhkxgIVsa01INgeGXVW1TkiUgdYKyIpwI/YFrMBQFXPiUgfYIrV17AGyCyS6mzgIaucdCaKyHkgP7ZHSZ2sPNeLSAKwOt22y/orwLZo0A8ishnb47U/MhOlqvNE5AZgpdWaOgX0wua43hGRNOACtn4WROQabC0xnw6hbXAtJuqsweBCRORnoKM3r6kuIoOAE6o6LseTDQGLeQxlMLiWJ4HynjYiB45h66Q3GLLEtCwMBoPBkCOmZWEwGAyGHDHOwmAwGAw5YpyFwWAwGHLEOAuDwWAw5IhxFgaDwWDIkf8Hs/cvXeBF7AkAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Conclusión:**\n",
        "\n",
        "El alfarero debe cobrar por sus vasijas $10 dólares para maximizar sus ganancias.\n",
        "\n",
        "Tanto el $lim_{p→10^-}\\:G(p)\\:$ como el $\\:lim_{p→10^+}\\:G(p)$ es igual a $1250$. Valor que indica las cantidad de ganancias máximas que puede obtener vendiendo $D(p)=750-50p$ vasijas a un precio $p$, teniendo en cuenta que le cuesta $5 dólares hacer una sóla pieza."
      ],
      "metadata": {
        "id": "zjc8va3rvh-g"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "----\n",
        "#<font color = 9ACD32>7.</font>\n",
        "Recall that the Heaviside function is defined by\n",
        "\n",
        "$$ H(t) = \\left\\{\\begin{matrix}\n",
        "0, & if\\:\\: t < 0, \\\\\n",
        "1, & if\\:\\: t \\geq 0.\n",
        "\\end{matrix}\\right. $$"
      ],
      "metadata": {
        "id": "2yfm0zIr_2y_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##A)\n",
        "\n",
        "Note that $H(−1) = 0$ and $H(1) = 1.$ Is there a point $c$ in $(−1, 1)$ such that $H(c) = 0.5$?"
      ],
      "metadata": {
        "id": "yphwFno9CcQv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def H(t):\n",
        "  if t < 0:\n",
        "    return 0\n",
        "  else:\n",
        "    return 1\n",
        "\n",
        "x = np.linspace(-5,5,100)\n",
        "y = np.array([H(xi) for xi in x])\n",
        "\n",
        "plt.xticks(range(-5,5))\n",
        "plt.yticks(np.arange(-1,1.25,0.25))\n",
        "plt.grid('-')\n",
        "\n",
        "plt.plot(x,y,'.')\n",
        "plt.show()\n",
        ""
      ],
      "metadata": {
        "id": "hftiP9XwDReJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "R/: $H(c)$ solo puede ser igual a $0$ o a $1$ dependiendo del valor de $c$,  debido a que es una función a trozos."
      ],
      "metadata": {
        "id": "X0YQ39x8HRW7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##B)\n",
        "Is the result of $A.$ consistent with the Intermediate Value Theorem?\n",
        "\n",
        "R/: No es consistente, ya que la función $H(t)$ no es continua, y por lo tanto, en el intervalo (-1,1) no hay punto intermedio."
      ],
      "metadata": {
        "id": "3iXWov4eJA2l"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##C)\n",
        "Does H attain a maximum value on [−1, 1]? Does H attain a minimum value on [−1, 1]?\n",
        "\n",
        "R/: $H(t)$ alcanza un valor maximo y un minimo constantes debido a las condiciones de la función a trozos. En el intervalo $[-1,1]$ el punto maximo de $H(t)$ es $1$ mientras $t \\geq 0$, y el punto minimo es $0$ mientras $t < 0$"
      ],
      "metadata": {
        "id": "H3YzmMYDLF4Z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##D)\n",
        "Are the results of (c) consistent with the Extreme Value Theorem?\n",
        "\n",
        "\n",
        "R/: No es consistente, ya que el teorema del valor extremo se enfoca en un intervalo continuo de la función, y $H(t)$ en $[-1,1]$ NO es continua."
      ],
      "metadata": {
        "id": "JTILfbRiMbQW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "----\n",
        "#<font color = 9ACD32>9.</font>\n",
        "Suppose $f$ and $g$ are continuous on $[0, 1], f(0) < g(0)$ and $f(1) > g(1)$. Show that there exists a point $c$ in the open interval $(0, 1)$ such that $f(c) = g(c)$."
      ],
      "metadata": {
        "id": "q9cSX0uKsCi8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Dado que $f$ y $g$ son funciones continuas en $[0,1]$, podemos usar el **teorema del valor intermedio** para probar que existe un punto $c$ en el intérvalo abierto de $(0,1)$ donde $f(c)=g(c)$.\n",
        "\n",
        "\n",
        ">La continuidad de la funciones en el intérvalo dado (Cumple para ambas funciones)\n",
        "\n",
        ">$m$ es un número cualquiera dentro de $f(a)\\: y \\:f(b)$ para el que existe un $c$ dentro del intérvalo $[a, b]$ donde $f(c)=m$\n",
        "\n",
        ">$n$ es un número cualquiera dentro de $g(a)\\: y \\: g(b)$ para el que existe un $c$ dentro del intérvalo $[a, b]$ donde $g(c)=n$\n",
        "\n",
        ">>Dado que $f(0) < g(0)$ y $f(1) > g(1)$ siendo $a=0$ y $b=1$, existe un c entre $[0,1]$ donde $m=n$\n",
        "\n",
        ">>Porque en algún punto $c$ dentro del intérvalo las gráficas van a intersectar\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "uQsQTsIW0W-e"
      }
    }
  ]
}