diff --git a/optimizacion/Enunciados/CryptOR.ipynb b/optimizacion/Enunciados/CryptOR.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# CryptOR"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<b><i style=\"font-size:13px\">Tags: </i></b><i style=\"font-size:11px\">Funciones a trozos</i>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Enunciado\n",
+    "CryptOR is una compañía que se dedica a minar criptomonedas. El mayor problema de planeación para CryptOR es la compra de energía. Dado el alto consumo de energía, CryptOR debe negociar contratos para los próximos 12 meses con las diferentes empresas de generación eléctrica. El costo por kilovatio-hora (kWh) varía según la cantidad de energía contratada y la empresa generadora. El costo total en función del consumo está representado por funciones no lineales suministradas por cada generadora. Así mismo, cada empresa generadora establece la duración de cada contrato que se firme con la misma y el consumo máximo mensual que pueden suministrar. Los contratos de cada generadora se pueden renovar múltiples veces durante los 12 meses de planeación, pero estos no se deben traslapar. Finalmente, se conoce un pronóstico de la demanda de energía en kWh que se debe satisfacer sin holgura. Las Tablas 1 y 2 resumen toda la información disponible. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tabla 1. Términos de los contratos para cada generadora.\n",
+    "\n",
+    "|                     |**Función de costo ($k)**                      | **Duración del contrato**| **Consumo máximo mensual**|\n",
+    "|:-------------------:|:----------------------------------------:|:------------------------:|:-------------------------:|\n",
+    "|**Generadora Carbón**|$f_1(x) = 0.0012 x^2$                     | 2 meses                  | 250 kWh                   |\n",
+    "|**Generadora Solar** |$f_2(x) = \\begin{cases}0.0028 x^2 - 0.5x + 35 \\ \\ x>0 \\\\ 0 \\ \\ x=0 \\end{cases}$          | 4 meses                  | 250 kWh                   |\n",
+    "|**Generadora Eólica**|$f_3(x) = \\begin{cases}0.5 x log(\\frac{x}{150}) + 30 \\ \\ x>0 \\\\ 0 \\ \\ x=0 \\end{cases}$  | 3 meses                  | 250 kWh                   |\n",
+    "\n",
+    "### Tabla 2. Demanda mensual en kWh.\n",
+    "|Mes| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12|\n",
+    "|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n",
+    "|demanda| 100| 150| 300| 300| 300| 500| 400| 400| 200| 200| 200| 200|"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1080x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "def f1(x):\n",
+    "    # Función de costo de la generadora carbón\n",
+    "    return 0.0012 * (x ** 2)\n",
+    "def f2(x):\n",
+    "    # Función de costo de la generadora solar\n",
+    "    return 0.0028 * x ** 2 - 0.5*x + 35\n",
+    "def f3(x):\n",
+    "    # Función de costo de la generadora eólica\n",
+    "    return 0.5 * x*np.log(x/150) + 30\n",
+    "\n",
+    "# Puntos de evaluación de la función\n",
+    "kwh = np.arange(1,250)\n",
+    "\n",
+    "fig, axs = plt.subplots(1,3, sharey=False, sharex=True, figsize=(15,5))\n",
+    "axs[0].plot(kwh, f1(kwh))\n",
+    "axs[1].plot(kwh, f2(kwh))\n",
+    "axs[2].plot(kwh, f3(kwh))\n",
+    "for ax_ix, ax in enumerate(axs):\n",
+    "    ax.set_xlabel(\"Consumo en kWh\")\n",
+    "    ax.set_ylabel(f\"f {ax_ix+1} (x)\")\n",
+    "    ax.set_ylim([0,100])\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Linealización a trozos\n",
+    "\n",
+    "Optimizar utilizando las funciones $f_1(x)$, $f_2(x)$ y $f_3(x)$ es computacionalmente más difícil debido a que son funciones no lineales. Sin embrago, dado que son funciones [convexas](https://es.wikipedia.org/wiki/Funci%C3%B3n_convexa) es posible aproximarlas con múltiples funciones lineales. Dada una función convexa $f(x)$, la función $g(x;x_0) = f(x_0) + f'(x_0) * (x-x0)$ es una aproximación de [primer orden](https://es.wikipedia.org/wiki/Serie_de_Taylor), la cual es exacta en $x_0$ y se degrada a medida que $x$ se aleja de $x_0$. Con esta idea en mente, cualquier función convexa se puede aproximar generando múltiples funciones de forma  $g(x;x_0)$ para diferentes valores de $x_0$. La siguiente celda muestra la función $f(x) = (x - 4)^2$ (en azul) y su aproximación (en rojo) utilizando 4 rectas correspondientes a  $g(x;x_0)$ para $x_0=0,3,5,8$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Función evaluada en 0:  16.0 + -8.0 * (x - 0)\n",
+      "Función evaluada en 3:  1.0 + -2.0 * (x - 3)\n",
+      "Función evaluada en 5:  1.0 + 2.0 * (x - 5)\n",
+      "Función evaluada en 8:  16.0 + 8.0 * (x - 8)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(-2.0, 40.0)"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1080x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "def f(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función (x-4) ^ 2\n",
+    "        return  (x-4) ** 2 \n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 2 *(x - 4)\n",
+    "\n",
+    "# Puntos de evaluacion de la función\n",
+    "dominio = np.arange(-2,10,0.01)\n",
+    "\n",
+    "fig, axs = plt.subplots(1,1, sharey=False, sharex=True, figsize=(15,5))\n",
+    "axs.plot(dominio, f(dominio))\n",
+    "for x_0 in [0, 3, 5, 8]:\n",
+    "    axs.plot(dominio, f(x_0) +  f(x_0,1) * (dominio - x_0), linestyle='dashed', color='red')\n",
+    "    print(f'Función evaluada en {x_0}:  {f(x_0):.1f} + {f(x_0, 1):.1f} * (x - {x_0})')\n",
+    "axs.set_xlabel(\"Consumo en kWh\")\n",
+    "axs.set_ylabel(f\"f(x)\")\n",
+    "axs.set_ylim([-2,40])\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Optimizando con la aproximación\n",
+    "Para una función convexa, $f(x)$, los siguientes problemas son equivalentes:\n",
+    " $$\n",
+    "\\begin{align*}\n",
+    "\\min & f(x)      &= \\ \\ \\min \\ \\ &z  \\\\ \n",
+    "&x\\in \\mathbb{R}. &        & z \\geq f(x), \\\\\n",
+    "&                &        & x \\in \\mathbb{R}.\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "Asi mismo, $f(x)\\geq g(x,x_0)$ para cualquier valor de $x_0$. \n",
+    "\n",
+    "Con estas dos observaciones, el problema original, $\\min_{x\\in\\mathbb{R}} (x-4)^2$, lo podemos aproximar con el siguiente modelo:\n",
+    " $$\n",
+    "\\begin{align*}\n",
+    "\\min \\ \\ &z  \\\\ \n",
+    "       & z \\geq 16  -8 * (x - 0) \\\\\n",
+    "       & z \\geq 1  -2 * (x - 3) \\\\\n",
+    "       & z \\geq 1 + 2 * (x - 5) \\\\\n",
+    "       & z \\geq 16 + 8 * (x - 8) \\\\\n",
+    "      & x \\in \\mathbb{R} \n",
+    "\\end{align*}\n",
+    "$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Funciones de costo aproximadas\n",
+    "Volviendo al problema de cryptOR, una posible aproximación se muestra a continuación. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Función 1 evaluada en 20:  0.480 + 0.048 * (x - 20)\n",
+      "Función 1 evaluada en 50:  3.000 + 0.120 * (x - 50)\n",
+      "Función 1 evaluada en 100:  12.000 + 0.240 * (x - 100)\n",
+      "Función 1 evaluada en 200:  48.000 + 0.480 * (x - 200)\n",
+      "Función 2 evaluada en 20:  26.120 + -0.388 * (x - 20)\n",
+      "Función 2 evaluada en 50:  17.000 + -0.220 * (x - 50)\n",
+      "Función 2 evaluada en 100:  13.000 + 0.060 * (x - 100)\n",
+      "Función 2 evaluada en 200:  47.000 + 0.620 * (x - 200)\n",
+      "Función 3 evaluada en 20:  9.851 + -0.507 * (x - 20)\n",
+      "Función 3 evaluada en 50:  2.535 + -0.049 * (x - 50)\n",
+      "Función 3 evaluada en 100:  9.727 + 0.297 * (x - 100)\n",
+      "Función 3 evaluada en 200:  58.768 + 0.644 * (x - 200)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1080x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "def f1(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función de costo de la generadora carbón\n",
+    "        return 0.0012 * (x ** 2) \n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 0.0012 * 2 * x\n",
+    "\n",
+    "def f2(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función de costo de la generadora solar\n",
+    "        return 0.0028 * x ** 2 - 0.5*x + 35\n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 2 * 0.0028 * x - 0.5\n",
+    "def f3(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función de costo de la generadora eólica\n",
+    "        return 0.5 * x*np.log(x/150) + 30\n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 0.5 * np.log(x/150) + 0.5\n",
+    "\n",
+    "# Funciones de costo\n",
+    "f = [f1,f2,f3]\n",
+    "# Puntos de evaluación de la función\n",
+    "kwh = np.arange(1,250)\n",
+    "\n",
+    "fig, axs = plt.subplots(1,3, sharey=False, sharex=True, figsize=(15,5))\n",
+    "for i, ax in enumerate(axs):\n",
+    "    axs[i].plot(kwh, f[i](kwh), )\n",
+    "    for x_0 in [20, 50, 100, 200]:\n",
+    "        axs[i].plot(kwh, f[i](x_0) +  f[i](x_0,1) * (kwh - x_0), linestyle='dashed', color='red')\n",
+    "        print(f'Función {i+1} evaluada en {x_0}:  {f[i](x_0):.3f} + {f[i](x_0, 1):.3f} * (x - {x_0})')\n",
+    "    ax.set_xlabel(\"Consumo en kWh\")\n",
+    "    ax.set_ylabel(f\"f {i+1} (x)\")\n",
+    "    ax.set_ylim([-1,100])\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Formule un modelo general de optimización lineal que le permita a CryptOR satisfacer la demanda de energía al mínimo costo y satisfaciendo las condiciones de los contratos. Para esto usted debe seguir los siguientes pasos: "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Formulación\n",
+    "\n",
+    "**1.** Escriba lo(s) conjunto(s), parámetro(s) y variable(s) de decisión que utilizará en el modelo.  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Restricciones\n",
+    "**2.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que se debe respetar la demanda exacta en cada mes. \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**3.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que la cantidad de kWh contratados no superan el consumo máximo mensual en los meses en donde hay un contrato vigente."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que si un contrato se firma, debe estar vigente por la duración estipulada, y que solo se puede haber un contrato vigente si se firmó previamente o en el mismo mes."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que los contratos con cada generadora no se deben traslapar."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) lineal(es) que modelan las funciones de costo con expresiones lineales. Note que si no hay un contrato vigente en un mes particular, el costo es cero."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) que describe(n) matemáticamente el tipo de variable(s) que está utilizando dentro del modelo. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Función Objetivo\n",
+    "**5.** Escriba la función objetivo."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Formulación matemática completa"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Implementación\n",
+    "**6.** Resuelva el modelo planteado utilizando la librería de PulP en Python. ¿Cuál es la solución\n",
+    "óptima del problema? "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#TODO: Implementación del modelo"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Créditos\n",
+    "Instancia: Daniel Duque<br>\n",
+    "Fecha: 21/12/2021"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/optimizacion/Soluciones/CryptOR.ipynb b/optimizacion/Soluciones/CryptOR.ipynb
new file mode 100644
index 0000000..4b6cadd
--- /dev/null
+++ b/optimizacion/Soluciones/CryptOR.ipynb
@@ -0,0 +1,690 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# CryptOR"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<b><i style=\"font-size:13px\">Tags: </i></b><i style=\"font-size:11px\">Funciones a trozos</i>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Enunciado\n",
+    "CryptOR is una compañía que se dedica a minar criptomonedas. El mayor problema de planeación para CryptOR es la compra de energía. Dado el alto consumo de energía, CryptOR debe negociar contratos para los próximos 12 meses con las diferentes empresas de generación eléctrica. El costo por kilovatio-hora (kWh) varía según la cantidad de energía contratada y la empresa generadora. El costo total en función del consumo está representado por funciones no lineales suministradas por cada generadora. Así mismo, cada empresa generadora establece la duración de cada contrato que se firme con la misma y el consumo máximo mensual que pueden suministrar. Los contratos de cada generadora se pueden renovar múltiples veces durante los 12 meses de planeación, pero estos no se deben traslapar. Finalmente, se conoce un pronóstico de la demanda de energía en kWh que se debe satisfacer sin holgura. Las Tablas 1 y 2 resumen toda la información disponible. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tabla 1. Términos de los contratos para cada generadora.\n",
+    "\n",
+    "|                     |**Función de costo ($k)**                      | **Duración del contrato**| **Consumo máximo mensual**|\n",
+    "|:-------------------:|:----------------------------------------:|:------------------------:|:-------------------------:|\n",
+    "|**Generadora Carbón**|$f_1(x) = 0.0012 x^2$                     | 2 meses                  | 250 kWh                   |\n",
+    "|**Generadora Solar** |$f_2(x) = \\begin{cases}0.0028 x^2 - 0.5x + 35 \\ \\ x>0 \\\\ 0 \\ \\ x=0 \\end{cases}$          | 4 meses                  | 250 kWh                   |\n",
+    "|**Generadora Eólica**|$f_3(x) = \\begin{cases}0.5 x log(\\frac{x}{150}) + 30 \\ \\ x>0 \\\\ 0 \\ \\ x=0 \\end{cases}$  | 3 meses                  | 250 kWh                   |\n",
+    "\n",
+    "### Tabla 2. Demanda mensual en kWh.\n",
+    "|Mes| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12|\n",
+    "|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n",
+    "|demanda| 100| 150| 300| 300| 300| 500| 400| 400| 200| 200| 200| 200|"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 413,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1080x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "def f1(x):\n",
+    "    # Función de costo de la generadora carbón\n",
+    "    return 0.0012 * (x ** 2)\n",
+    "def f2(x):\n",
+    "    # Función de costo de la generadora solar\n",
+    "    return 0.0028 * x ** 2 - 0.5*x + 35\n",
+    "def f3(x):\n",
+    "    # Función de costo de la generadora eólica\n",
+    "    return 0.5 * x*np.log(x/150) + 30\n",
+    "\n",
+    "# Puntos de evaluación de la función\n",
+    "kwh = np.arange(1,250)\n",
+    "\n",
+    "fig, axs = plt.subplots(1,3, sharey=False, sharex=True, figsize=(15,5))\n",
+    "axs[0].plot(kwh, f1(kwh))\n",
+    "axs[1].plot(kwh, f2(kwh))\n",
+    "axs[2].plot(kwh, f3(kwh))\n",
+    "for ax_ix, ax in enumerate(axs):\n",
+    "    ax.set_xlabel(\"Consumo en kWh\")\n",
+    "    ax.set_ylabel(f\"f {ax_ix+1} (x)\")\n",
+    "    ax.set_ylim([0,100])\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Linealización a trozos\n",
+    "\n",
+    "Optimizar utilizando las funciones $f_1(x)$, $f_2(x)$ y $f_3(x)$ es computacionalmente más difícil debido a que son funciones no lineales. Sin embrago, dado que son funciones [convexas](https://es.wikipedia.org/wiki/Funci%C3%B3n_convexa) es posible aproximarlas con múltiples funciones lineales. Dada una función convexa $f(x)$, la función $g(x;x_0) = f(x_0) + f'(x_0) * (x-x0)$ es una aproximación de [primer orden](https://es.wikipedia.org/wiki/Serie_de_Taylor), la cual es exacta en $x_0$ y se degrada a medida que $x$ se aleja de $x_0$. Con esta idea en mente, cualquier función convexa se puede aproximar generando múltiples funciones de forma  $g(x;x_0)$ para diferentes valores de $x_0$. La siguiente celda muestra la función $f(x) = (x - 4)^2$ (en azul) y su aproximación (en rojo) utilizando 4 rectas correspondientes a  $g(x;x_0)$ para $x_0=0,3,5,8$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 414,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Función evaluada en 0:  16.0 + -8.0 * (x - 0)\n",
+      "Función evaluada en 3:  1.0 + -2.0 * (x - 3)\n",
+      "Función evaluada en 5:  1.0 + 2.0 * (x - 5)\n",
+      "Función evaluada en 8:  16.0 + 8.0 * (x - 8)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(-2.0, 40.0)"
+      ]
+     },
+     "execution_count": 414,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1080x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "def f(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función (x-4) ^ 2\n",
+    "        return  (x-4) ** 2 \n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 2 *(x - 4)\n",
+    "\n",
+    "# Puntos de evaluacion de la función\n",
+    "dominio = np.arange(-2,10,0.01)\n",
+    "\n",
+    "fig, axs = plt.subplots(1,1, sharey=False, sharex=True, figsize=(15,5))\n",
+    "axs.plot(dominio, f(dominio))\n",
+    "for x_0 in [0, 3, 5, 8]:\n",
+    "    axs.plot(dominio, f(x_0) +  f(x_0,1) * (dominio - x_0), linestyle='dashed', color='red')\n",
+    "    print(f'Función evaluada en {x_0}:  {f(x_0):.1f} + {f(x_0, 1):.1f} * (x - {x_0})')\n",
+    "axs.set_xlabel(\"Consumo en kWh\")\n",
+    "axs.set_ylabel(f\"f(x)\")\n",
+    "axs.set_ylim([-2,40])\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Optimizando con la aproximación\n",
+    "Para una función convexa, $f(x)$, los siguientes problemas son equivalentes:\n",
+    " $$\n",
+    "\\begin{align*}\n",
+    "\\min & f(x)      &= \\ \\ \\min \\ \\ &z  \\\\ \n",
+    "&x\\in \\mathbb{R}. &        & z \\geq f(x), \\\\\n",
+    "&                &        & x \\in \\mathbb{R}.\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "Asi mismo, $f(x)\\geq g(x,x_0)$ para cualquier valor de $x_0$. \n",
+    "\n",
+    "Con estas dos observaciones, el problema original, $\\min_{x\\in\\mathbb{R}} (x-4)^2$, lo podemos aproximar con el siguiente modelo:\n",
+    " $$\n",
+    "\\begin{align*}\n",
+    "\\min \\ \\ &z  \\\\ \n",
+    "       & z \\geq 16  -8 * (x - 0) \\\\\n",
+    "       & z \\geq 1  -2 * (x - 3) \\\\\n",
+    "       & z \\geq 1 + 2 * (x - 5) \\\\\n",
+    "       & z \\geq 16 + 8 * (x - 8) \\\\\n",
+    "      & x \\in \\mathbb{R} \n",
+    "\\end{align*}\n",
+    "$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Funciones de costo aproximadas\n",
+    "Volviendo al problema de cryptOR, una posible aproximación se muestra a continuación. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 415,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Función 1 evaluada en 20:  0.480 + 0.048 * (x - 20)\n",
+      "Función 1 evaluada en 50:  3.000 + 0.120 * (x - 50)\n",
+      "Función 1 evaluada en 100:  12.000 + 0.240 * (x - 100)\n",
+      "Función 1 evaluada en 200:  48.000 + 0.480 * (x - 200)\n",
+      "Función 2 evaluada en 20:  26.120 + -0.388 * (x - 20)\n",
+      "Función 2 evaluada en 50:  17.000 + -0.220 * (x - 50)\n",
+      "Función 2 evaluada en 100:  13.000 + 0.060 * (x - 100)\n",
+      "Función 2 evaluada en 200:  47.000 + 0.620 * (x - 200)\n",
+      "Función 3 evaluada en 20:  9.851 + -0.507 * (x - 20)\n",
+      "Función 3 evaluada en 50:  2.535 + -0.049 * (x - 50)\n",
+      "Función 3 evaluada en 100:  9.727 + 0.297 * (x - 100)\n",
+      "Función 3 evaluada en 200:  58.768 + 0.644 * (x - 200)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1080x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "def f1(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función de costo de la generadora carbón\n",
+    "        return 0.0012 * (x ** 2) \n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 0.0012 * 2 * x\n",
+    "\n",
+    "def f2(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función de costo de la generadora solar\n",
+    "        return 0.0028 * x ** 2 - 0.5*x + 35\n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 2 * 0.0028 * x - 0.5\n",
+    "def f3(x, orden=0):\n",
+    "    if orden == 0:\n",
+    "        # Función de costo de la generadora eólica\n",
+    "        return 0.5 * x*np.log(x/150) + 30\n",
+    "    else:\n",
+    "        # Derivada evaluada en x\n",
+    "        return 0.5 * np.log(x/150) + 0.5\n",
+    "\n",
+    "# Funciones de costo\n",
+    "f = [f1,f2,f3]\n",
+    "# Puntos de evaluación de la función\n",
+    "kwh = np.arange(1,250)\n",
+    "\n",
+    "fig, axs = plt.subplots(1,3, sharey=False, sharex=True, figsize=(15,5))\n",
+    "for i, ax in enumerate(axs):\n",
+    "    axs[i].plot(kwh, f[i](kwh), )\n",
+    "    for x_0 in [20, 50, 100, 200]:\n",
+    "        axs[i].plot(kwh, f[i](x_0) +  f[i](x_0,1) * (kwh - x_0), linestyle='dashed', color='red')\n",
+    "        print(f'Función {i+1} evaluada en {x_0}:  {f[i](x_0):.3f} + {f[i](x_0, 1):.3f} * (x - {x_0})')\n",
+    "    ax.set_xlabel(\"Consumo en kWh\")\n",
+    "    ax.set_ylabel(f\"f {i+1} (x)\")\n",
+    "    ax.set_ylim([-1,100])\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Formule un modelo general de optimización lineal que le permita a CryptOR satisfacer la demanda de energía al mínimo costo y satisfaciendo las condiciones de los contratos. Para esto usted debe seguir los siguientes pasos:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Formulación\n",
+    "\n",
+    "**1.** Escriba lo(s) conjunto(s), parámetro(s) y variable(s) de decisión que utilizará en el modelo.  \n",
+    "\n",
+    "### Conjuntos\n",
+    "- $P$: Generadoras\n",
+    "- $T$: Periodos de planeación\n",
+    "\n",
+    "### Parámetros\n",
+    "- $d_t$: demanda de energía en kWh para el mes $t\\in T$\n",
+    "- $b_i$: Consumo máximo mensual de la generadora $i\\in G$\n",
+    "- $m_i$: Duración de cada contrato de la generadora $i\\in G$\n",
+    "- $a_{ik}$: intercepto de la ecuación $k\\in\\{1,2,3,4\\}$ para la generadora $i\\in G$\n",
+    "- $p_{ik}$: pendiente de la ecuación $k\\in\\{1,2,3,4\\}$ para la generadora $i\\in G$\n",
+    "\n",
+    "### Variables de decisión\n",
+    "- $x_{it}$: cantidad de kWh contratados a la generadora $i\\in G$ para el mes $t\\in T$\n",
+    "- $y_{it}$: variable binaria que indica si un nuevo contrato se firma con la generadora $i\\in G$ en el mes $t\\in T$\n",
+    "- $v_{it}$: variable binaria que indica si un contrato con la generadora $i\\in G$ esta vigente en el mes $t\\in T$\n",
+    "- $z_{it}$: costo total por consumo de energía de la generadora $i\\in G$ en el mes $t\\in T$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Restricciones\n",
+    "**2.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que se debe respetar la demanda exacta en cada mes. \n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\sum_{i \\in G}x_{it} = d_t \\ \\ \\forall t \\in T.\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**3.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que la cantidad de kWh contratados no superan el consumo máximo mensual en los meses en donde hay un contrato vigente.\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "x_{it} \\leq b_i v_{it} \\forall i \\in G, t \\in T.\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que si un contrato se firma, debe estar vigente por la duración estipulada, y que solo se puede haber un contrato vigente si se firmó previamente o en el mismo mes.\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\sum_{t' \\in \\{\\max\\{t-m_i+1, 1\\}, \\ldots, t\\}}y_{it'} \\geq  v_{it} \\ \\ \\forall i \\in G, t \\in T. \\\\ \n",
+    "|\\{t, \\ldots, \\min\\{t+m_i-1,12\\}\\}|y_{it} \\leq  \\sum_{t' \\in \\{t, \\ldots, \\min\\{t+m_i-1,12\\}\\}}v_{it} \\ \\ \\forall i \\in G, t \\in T. \\\\ \n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) lineal(es) que garantiza(n) que los contratos con cada generadora no se deben traslapar.\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\sum_{t' \\in \\{t, \\ldots, t+m_i-1\\}}y_{it'} \\leq 1 \\ \\ \\forall i \\in G, t \\in T.\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) lineal(es) que modelan las funciones de costo con expresiones lineales. Note que si no hay un contrato vigente en un mes particular, el costo es cero.\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "z_{it} \\geq a_{ik} + p_{ik} x_{it} - M(1-v_{it})  \\ \\ \\forall i \\in G, t \\in T, k \\in \\{1,2,3,4\\}\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Escriba la(s) restricción(es) que describe(n) matemáticamente el tipo de variable(s) que está utilizando dentro del modelo. \n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "x_{it} & \\ge 0 \\ \\ &&\\forall i\\in G,t\\in T.\\\\\n",
+    "y_{it} & \\in\\{0,1\\} \\ \\ &&\\forall i\\in G,t\\in T.\\\\\n",
+    "v_{it} & \\in \\{0,1\\} \\ \\  &&\\forall i\\in G,t\\in T.\\\\\n",
+    "z_{it} & \\ge 0 \\ \\ &&\\forall i\\in G,t\\in D.\\\\\n",
+    "\\end{align*}\n",
+    "$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Función Objetivo\n",
+    "**5.** Escriba la función objetivo.\n",
+    "\n",
+    "$$\n",
+    "\\text{minimizar }  \\sum_{i\\in P}\\sum_{t\\in T}z_{it}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Formulación matemática completa"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Formulación\n",
+    "\n",
+    "**1.** Escriba lo(s) conjunto(s), parámetro(s) y variable(s) de decisión que utilizará en el modelo.  \n",
+    "\n",
+    "### Conjuntos\n",
+    "- $P$: Generadoras\n",
+    "- $T$: Periodos de planeación\n",
+    "\n",
+    "### Parámetros\n",
+    "- $d_t$: demanda de energía en kWh para el mes $t\\in T$\n",
+    "- $b_i$: Consumo máximo mensual de la generadora $i\\in G$\n",
+    "- $m_i$: Duración de cada contrato de la generadora $i\\in G$\n",
+    "- $a_{ik}$: intercepto de la ecuación $k\\in\\{1,2,3,4\\}$ para la generadora $i\\in G$\n",
+    "- $p_{ik}$: pendiente de la ecuación $k\\in\\{1,2,3,4\\}$ para la generadora $i\\in G$\n",
+    "\n",
+    "### Variables de decisión\n",
+    "- $x_{it}$: cantidad de kWh contratados a la generadora $i\\in G$ para el mes $t\\in T$\n",
+    "- $y_{it}$: variable binaria que indica si un nuevo contrato se firma con la generadora $i\\in G$ en el mes $t\\in T$\n",
+    "- $v_{it}$: variable binaria que indica si un contrato con la generadora $i\\in G$ está vigente en el mes $t\\in T$\n",
+    "- $z_{it}$: costo total por consumo de energía de la generadora $i\\in G$ en el mes $t\\in T$\n",
+    "\n",
+    "**Modelo:**\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\n",
+    "&\\text{minimizar } & \\sum_{i\\in P}\\sum_{t\\in T}z_{it} &&(1)\\\\\n",
+    "&\\text{sujeto a}&&& \\\\\n",
+    "&&\\sum_{i \\in G}x_{it} = d_t \\ \\  \\ \\  & \\forall t \\in T; &(2) \\\\\n",
+    "&&x_{it} \\leq b_i v_{it}  \\ \\  \\ \\  & \\forall i \\in G, t \\in T;&(3)\\\\\n",
+    "&&\\sum_{t' \\in \\{\\max\\{t-m_i+1, 1\\}, \\ldots, t\\}}y_{it'} \\geq  v_{it}  \\ \\  \\ \\  & \\forall i \\in G, t \\in T; &(4)\\\\ \n",
+    "&&|\\{t, \\ldots, \\min\\{t+m_i-1,12\\}\\}|y_{it} \\leq  \\sum_{t' \\in \\{t, \\ldots, \\min\\{t+m_i-1,12\\}\\}}v_{it}  \\ \\  \\ \\  & \\forall i \\in G, t \\in T;&(5)\\\\\n",
+    "&&\\sum_{t' \\in \\{t, \\ldots, t+m_i-1\\}}y_{it'} \\leq 1  \\ \\  \\ \\  & \\forall i \\in G, t \\in T;&(6) \\\\ \n",
+    "&&z_{it} \\geq a_{ik} + p_{ik} x_{it} - M(1-v_{it})   \\ \\  \\ \\  & \\forall i \\in G, t \\in T, k \\in \\{1,2,3,4\\};&(7) \\\\\n",
+    "&&x_{it}  \\ge 0  \\ \\  \\ \\  &\\forall i\\in G,t\\in T; &(8)\\\\\n",
+    "&&y_{it}  \\in\\{0,1\\}  \\ \\  \\ \\  &\\forall i\\in G,t\\in T;\\\\\n",
+    "&&v_{it}  \\in \\{0,1\\}   \\ \\  \\ \\  &\\forall i\\in G,t\\in T;\\\\\n",
+    "&&z_{it}  \\ge 0  \\ \\  \\ \\  &\\forall i\\in G,t\\in D.\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Implementación\n",
+    "**6.** Resuelva el modelo planteado utilizando la librería de PulP en Python. ¿Cuál es la solución\n",
+    "óptima del problema? "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 416,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Estado (optimizador): Optimal\n",
+      "\n",
+      " Costos totales = $ 123.29\n",
+      "\n",
+      "Variables de decisión\n",
+      "Mes               1       2       3       4       5       6       7       8       9      10      11      12\n",
+      "Generadora 1    27.87   77.87   77.87   50.00   25.00   25.00  150.00   27.87   27.87   27.87   27.87   27.87\n",
+      "Nuevo             1       0       1       0       1       0       1       0       1       0       1       0\n",
+      "Vigente           1       1       1       1       1       1       1       1       1       1       1       1\n",
+      "Generadora 2     0.00    0.00    0.00  150.00   75.00   75.00  150.00    0.00    0.00    0.00    0.00    0.00\n",
+      "Nuevo             0       0       0       1       0       0       0       0       0       0       0       0\n",
+      "Vigente           0       0       0       1       1       1       1       0       0       0       0       0\n",
+      "Generadora 3    72.13   72.13   72.13    0.00    0.00    0.00  100.00   72.13   72.13   72.13   72.13   72.13\n",
+      "Nuevo             1       0       0       0       0       0       1       0       0       1       0       0\n",
+      "Vigente           1       1       1       0       0       0       1       1       1       1       1       1\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Importar librerías\n",
+    "import pulp as lp\n",
+    "import numpy as np\n",
+    "from itertools import product\n",
+    "\n",
+    "#-----------------\n",
+    "# Conjuntos\n",
+    "#-----------------\n",
+    "# Generadoras\n",
+    "G=[\"Generadora 1\",\"Generadora 2\",\"Generadora 3\"]\n",
+    "\n",
+    "# Periodos de planeación\n",
+    "T = list(range(1,12+1)) # range excluye el final del intervalo.\n",
+    "\n",
+    "# Conjunto de tuplas (i,t) donde i es una generadora\n",
+    "# en G y t es un periodo de tiempo en T. \n",
+    "G_x_T = list(product(G,T))\n",
+    "\n",
+    "#-----------------\n",
+    "# Parámetros\n",
+    "#-----------------\n",
+    "d={# Periodo: demanda en kWh\n",
+    "   1: 100, 2: 150, 3: 150, 4: 200, 5: 100, 6: 100,\n",
+    "   7: 400, 8: 100, 9: 100, 10: 100, 11: 100, 12: 100} \n",
+    "b={# Generadora: consumo maximo en kWh\n",
+    "   \"Generadora 1\":250,\n",
+    "   \"Generadora 2\":250,\n",
+    "   \"Generadora 3\":250}\n",
+    "\n",
+    "m={# Generadora: duración de por contrato en meses\n",
+    "   \"Generadora 1\":2,\n",
+    "   \"Generadora 2\":4,\n",
+    "   \"Generadora 3\":3}\n",
+    "\n",
+    "# Funciones de aproximación\n",
+    "# Función 1 evaluada en 20:  0.480 + 0.048 * (x - 20)\n",
+    "# Función 1 evaluada en 50:  3.000 + 0.120 * (x - 50)\n",
+    "# Función 1 evaluada en 100:  12.000 + 0.240 * (x - 100)\n",
+    "# Función 1 evaluada en 200:  48.000 + 0.480 * (x - 200)\n",
+    "# Función 2 evaluada en 20:  26.120 + -0.388 * (x - 20)\n",
+    "# Función 2 evaluada en 50:  17.000 + -0.220 * (x - 50)\n",
+    "# Función 2 evaluada en 100:  13.000 + 0.060 * (x - 100)\n",
+    "# Función 2 evaluada en 200:  47.000 + 0.620 * (x - 200)\n",
+    "# Función 3 evaluada en 20:  9.851 + -0.507 * (x - 20)\n",
+    "# Función 3 evaluada en 50:  2.535 + -0.049 * (x - 50)\n",
+    "# Función 3 evaluada en 100:  9.727 + 0.297 * (x - 100)\n",
+    "# Función 3 evaluada en 200:  58.768 + 0.644 * (x - 200)\n",
+    "f={#Generadora: lista de tuplas (a,p), donde \"a\" es el \n",
+    "   #            intercepto y \"p\" la pendiente de una función\n",
+    "   #            aproximando el costo de la generadora\n",
+    "   \"Generadora 1\":[(0.48 - 0.048*20, 0.048),\n",
+    "                   (3.0 - 0.12*50, 0.12),\n",
+    "                   (12 - 0.24*100, 0.24),\n",
+    "                   (48 - 0.48*200, 0.48)],\n",
+    "   \"Generadora 2\":[(26.12 + 0.388*20, -0.388),\n",
+    "                   (17 + 0.22*50, -0.22),\n",
+    "                   (13 - 0.06*100, 0.06),\n",
+    "                   (47 - 0.62*200, 0.62)],\n",
+    "   \"Generadora 3\":[(9.851 + 0.507*20, -0.507),\n",
+    "                   (2.535 + 0.049*50, -0.049),\n",
+    "                   (9.727 - 0.297*100 , 0.297),\n",
+    "                   (58.768 - 0.644*200, 0.644)]}\n",
+    "\n",
+    "#-------------------------------------\n",
+    "# Creación del objeto problema en PuLP\n",
+    "#-------------------------------------\n",
+    "#Crea el problema para cargarlo con la instancia \n",
+    "problema=lp.LpProblem(\"CryptOT\",lp.LpMinimize)\n",
+    "\n",
+    "#-----------------------------\n",
+    "# Variables de Decisión\n",
+    "#-----------------------------\n",
+    "# Consumo mensual (en kWh) de la generadora i en G en el periodo\n",
+    "# de tiempo t en T\n",
+    "limite_superior_x = np.max([b[i] for i in G])\n",
+    "x=lp.LpVariable.dicts('x', G_x_T, lowBound=0, upBound=limite_superior_x,\n",
+    "                      cat=lp.const.LpContinuous)\n",
+    "\n",
+    "# Variable binaria que indica si un nuevo contrato es firmado con la\n",
+    "# generadora i en G en el periodo de tiempo t en T\n",
+    "y=lp.LpVariable.dicts('y', G_x_T, cat=lp.const.LpBinary)\n",
+    "\n",
+    "# Variable binaria que indica si hay un contrato vigente con la\n",
+    "# generadora i en G en el periodo de tiempo t en T\n",
+    "v=lp.LpVariable.dicts('v', G_x_T, cat=lp.const.LpBinary)\n",
+    "\n",
+    "\n",
+    "# Variable auxiliar para calcular el costo por consumo asociado\n",
+    "# a la generadora i en G en el periodo de tiempo t en T\n",
+    "z=lp.LpVariable.dicts('z', G_x_T, lowBound=0, cat=lp.const.LpContinuous)\n",
+    "\n",
+    "#-----------------------------\n",
+    "# Función objetivo\n",
+    "#-----------------------------\n",
+    "#Crea la expresión de minimización de costos\n",
+    "problema+=lp.lpSum(z[i,t] for i in G for t in T), \"Costo anual\"\n",
+    "\n",
+    "#-----------------------------\n",
+    "# Restricciones\n",
+    "#-----------------------------\n",
+    "\n",
+    "\n",
+    "# Satisfacción de la demanda\n",
+    "# sum(i in G)x_it = d_t forall t in T\n",
+    "for t in T:\n",
+    "    problema+= lp.lpSum(x[i,t] for i in G) == d[t], f\"Satisfacción de la demanda en el mes {t}\" \n",
+    "\n",
+    "# Relación entre consumo y contratos vigentes\n",
+    "# x_it <= b_i * v_it forall i in G, t in T\n",
+    "for (i,t) in G_x_T:\n",
+    "    problema+= x[i,t] <= b[i]*v[i,t], f\"Consumo de la generadora {i} en el mes {t}\" \n",
+    "\n",
+    "# Duracion de los contratos\n",
+    "for (i,t) in G_x_T:\n",
+    "    # Periodos en los que podría ser firmado un contrato para que este vigente en t.\n",
+    "    T_f = [tt for tt in range(t - m[i] + 1, t + 1) if tt>=1] \n",
+    "    problema+= sum(y[i,tt] for tt in T_f) >= v[i,t], f\"Vigencia en el mes {t} de contratos de la Generadora {i} parte 1\"\n",
+    "    # Periodos vigentes si se firma un contrato en t\n",
+    "    T_v = [tt for tt in range(t, t + m[i]) if tt<=12] \n",
+    "    problema+= len(T_v) * y[i,t] <= sum(v[i,tt] for tt in T_v), f\"Vigencia en el mes {t} de contratos de la Generadora {i} parte 2\"\n",
+    "\n",
+    "# Máximo un contrato vigente por generadora en cada mes\n",
+    "# sum(tt in [t, ..., t+m_i-1])y_i,tt <= 1 forall i in G, t in T\n",
+    "for (i,t) in G_x_T:\n",
+    "    # Periodos vigentes si se firma un contrato en t\n",
+    "    T_v = [tt for tt in range(t, t + m[i]) if tt<=12] \n",
+    "    problema+= lp.lpSum(y[i,tt] for tt in T_v) <= 1, f\"Limite de nuevos contratos de la Generadora {i} firmados en el mes {t}\" \n",
+    "\n",
+    "# Función aproximada a trozos\n",
+    "# z_it >= a_ik * p_ik * x_it - M(1-v_it)forall i in G, t in T, k = 1,...,numero_de_funciones\n",
+    "M = 100\n",
+    "for (i,t) in G_x_T:\n",
+    "    for k, (a,p) in enumerate(f[i]):\n",
+    "        problema+= z[i,t] >= a+ p*x[i,t] - M * (1-v[i,t]), f\"Aproximación {k} del costo por consumo de la generadora {i} en el mes {t}\" \n",
+    "\n",
+    "#-----------------------------\n",
+    "# Imprimir formato LP\n",
+    "#-----------------------------\n",
+    "#Escribe el problema en un archivo con formato LP \n",
+    "problema.writeLP(\"CryptOR.lp\")\n",
+    "\n",
+    "#-----------------------------\n",
+    "# Invocar el optimizador\n",
+    "#-----------------------------\n",
+    "#Optimizar el modelo con CBC (default de PuLP)\n",
+    "problema.solve()\n",
+    "\n",
+    "#-----------------------------\n",
+    "#    Imprimir resultados\n",
+    "#-----------------------------\n",
+    "#Imprimir estado final del optimizador\n",
+    "print(\"Estado (optimizador):\", lp.LpStatus[problema.status],end='\\n')\n",
+    "\n",
+    "#Valor óptimo del plan de transporte  \n",
+    "print(\"\\n Costos totales = $\", round(lp.value(problema.objective),2))\n",
+    "print()\n",
+    "\n",
+    "#Imprimir variables de decisión\n",
+    "print(\"Variables de decisión\")\n",
+    "tap_ = \"\"\n",
+    "print(f'{\"Mes\":10s} {tap_.join(f\"{t:>8d}\" for t in T)}')\n",
+    "    \n",
+    "for i in G:\n",
+    "    print(f'{i:10s} {tap_.join(f\"{x[i,t].value():>8.2f}\" for t in T)}')\n",
+    "    print(f'{\"Nuevo\":10s} {tap_.join(f\"{y[i,t].value():>8.0f}\" for t in T)}')\n",
+    "    print(f'{\"Vigente\":10s} {tap_.join(f\"{v[i,t].value():>8.0f}\" for t in T)}')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Créditos\n",
+    "Instancia: Daniel Duque<br>\n",
+    "Fecha: 21/12/2021"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
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+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
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