{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Le problème du vendeur de journaux (à une période de temps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Chaque matin, le vendeur doit décider d’un nombre de journaux à commander $u ∈ 𝕌 = {0, 1,\\ldots}$ au prix unitaire $c > 0$. La demande du jour est incertaine $w ∈ 𝕎 = {0, 1,\\ldots}$.\n",
    "\n",
    "Si à la fin de la journée il lui reste des invendus (coût unitaire $c_S ∈ ℝ$):\n",
    "$$c_S(u − w )_+ = c_S \\max (u − w,0)$$\n",
    "On suppose que $c > − c_S$.\n",
    "\n",
    "Si à la fin de la journée il n’a pas pu faire face à la demande on associe un coût unitaire $c_M$. Le coût lié à la non satisfaction de la demande est:\n",
    "$$c_M (w − u )_+ = c_M \\max (w − u,0).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np;\n",
    "from scipy.special import comb;\n",
    "from scipy.special import gamma;\n",
    "import matplotlib.pyplot as plt\n",
    "import io;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [],
   "source": [
    "binomiale=1\n",
    "discrete=2\n",
    "poisson=3\n",
    "\n",
    "def choisir_loi(law):\n",
    "\n",
    "    if law == binomiale:  ## loi binomiale\n",
    "        n=100\n",
    "        p=0.5\n",
    "\n",
    "        buf = io.StringIO()\n",
    "        buf.write(\"loi binomiale(%d,%5.2f)\" % (n,p))\n",
    "        title = buf.getvalue()\n",
    "    \n",
    "        wi = np.linspace(0,n,num=n+1) ## les valeurs possibles {0,1,...,n}\n",
    "        ## pdf(\"bin\",x,n,p) = n!/x!(n-x)! p^x (1-p)^n-x \n",
    "        nn = n*np.ones(n+1)\n",
    "        pi=comb(nn,wi, exact=False) * pow(p,wi)*pow(1-p,n-wi)\n",
    "\n",
    "        mu=n*p; ## moyenne de la binomiale \n",
    "        mu1= sum(pi*wi) ; ## vérification \n",
    "        if abs(mu-mu1) > 1.e-8:\n",
    "            print(\"something wrong in binomial law expectation\")\n",
    "            wait = input(\"PRESS ENTER TO CONTINUE.\")\n",
    "    \n",
    "        # un echantillong de taille N\n",
    "        N=1000\n",
    "        #W=grand(1,N,\"bin\",n,p);\n",
    "        W = np.random.binomial(n, p, N)\n",
    " \n",
    "    if law == discrete: ## une loi discrète \n",
    "        n=3\n",
    "        wi=np.array([30,50,80])\n",
    "        # A vous\n",
    "        # pi = choisir des probabilités\n",
    "        buf = io.StringIO()\n",
    "        buf.write(\"loi discrète sur %d valeurs\" % wi.size)\n",
    "        title = buf.getvalue()\n",
    "        # A vous : mu= ## la moyenne\n",
    "\n",
    "        N=1000\n",
    "        # un echantillong de taille N\n",
    "        # A vous : tirer un échantillon de taille N\n",
    "    \n",
    "    if law == poisson: ## loi de Poisson de paramètre mu \n",
    "        n=100;\n",
    "        p=0.5;\n",
    "        mu=n*p;\n",
    "        wi=np.linspace(0,n,num=n+1); ## les valeurs possibles \n",
    "        pi=( pow(mu,wi) *np.exp(-mu)) / gamma(wi+1);\n",
    "        buf = io.StringIO();\n",
    "        buf.write(\"Poisson %f\" % mu);\n",
    "        title = buf.getvalue();\n",
    "        # A vous : \n",
    "        #     calculer la moyenne theorique, \n",
    "        #     tirer un echantillon de taille N, \n",
    "        #     comparer avec la moyenne empirique\n",
    "\n",
    "    return pi, wi, W, title\n",
    "\n",
    "def hist_plot(samples,support=[]):\n",
    "    if np.size(support)==0:\n",
    "        support = np.sort(list(dict.fromkeys(samples)))\n",
    "    histo=np.zeros(support.size);\n",
    "    for i in range(support.size):\n",
    "        histo[i]=np.size(np.where(samples==support[i]))/(W.size)\n",
    "    # On trace cet histogramme\n",
    "    plt.bar(support, histo,width=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pi, wi, W, title = choisir_loi(poisson) # poisson, binomiale, discrete\n",
    "\n",
    "fig = plt.gcf()\n",
    "\n",
    "#plt.subplot(1,3,1);\n",
    "plt.bar(wi,pi,width=1)\n",
    "plt.title(\"loi\"); \n",
    "plt.show()\n",
    "\n",
    "#plt.subplot(1,3,2);\n",
    "plt.step(wi,np.cumsum(pi),where='post',marker='o',markerfacecolor='r');\n",
    "plt.title(\"cdf :\" + title)\n",
    "plt.show()\n",
    "\n",
    "#plt.subplot(1,3,3);\n",
    "hist_plot(W,wi)\n",
    "plt.title(\"loi empirique\"); \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Paragraph 1.2__ On utilise tout d’abord la distribution de Poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__1.1 La demande aléatoire__\n",
    "\n",
    "On veut faire tourner le même code pour plusieurs lois distinctes qui seront des lois discrètes. La valeur de law permet de selctionner une loi au choix: loi _binomiale_, loi _discrete_, loi de _Poisson_.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "pi, wi, W, title = choisir_loi(poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Question 2.__ Écrire une fonction Python qui calcule j(u,w) puis une fonction qui calcule J(u). Faire un graphique avec les valeurs proposées des constantes et calculer le nombre de journaux qu’il faut commander "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cas discrêt: Nombre optimal de journaux a commander *30.000000*, Moyenne de la demande *47.500000*\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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zEng5ZvyaIA00ENgVnCJ6A/iWmTUJPvz9VjCWlD6Ph368md8rHiqSEmYuL2TW8iJuGtxNsc8yKnUyODObCgwCmptZAZE0z73Ac2Y2BlgPXBos/hpwPpAP7ANGA7j7djP7NTAvWO5X7h7/wXJSGfuNLqzZuo9HZq2ic7N6XNZPs4eKJKviIPbZKcMv8l5epTYAdx9xlIcGH2FZB244ys+ZAEwoV3Uh+tLsoS9+TNsmdTlds4eKJKUpc9eTX7iHx6/JVeyzHPQvdQzReOjxOfUVDxVJUtHY5+ldm3HOiS1Kf4J8Tg2gFA3r1GT8qFzFQ0WSlGKfFacGUAbR2UMVDxVJLtHY54j+HejRSrHP8lIDKKPI7KGn8FHBTn703ALFQ0WSwD2KfSZEDaAchvRuxc+GnshrH3+ieKhIyKKzfd40uBvNFPuskIy5JnBlue4bnVmzbS+PzFpFp2bZXN6vQ9gliWScvQcO8evgIu+KfVacGkA5mRm/uqgXBTv2c/uLi2jXJFvxUJFqtO/gIa6dOI+12/bx5Kh+in0mQP9yFVAj6zgeuuIUxUNFqtlnxYcZ+1Qe89Zu54+XncSZJ1TvfGHpRg2gghrUqcmE0f2oU1PxUJHqED34v7tqG3+49CSGnXzECYWlHNQAEtC2cV3FQ0WqwYFDh7l+8ge8s3Irv72kD5f0bRd2SWlBDSBBfdopHipSlYoPl/CDKR/y1rJCfvNfX9O8XJVIDaASKB4qUjWKD5dw09QPeXPJFn41rBdXDFDqrjIpBVRJYuOhHZtmM7y/flFFEnHocAm3PLuA1xd9wh0X9OSar3cKu6S0owZQSb4UD30pEg89o5vioSIVcbjE+e+/fsTfF27mtqE9GHNG57BLSks6BVSJovHQrjn1+f5kxUNFKqKkxPnp3xby0oJN/OS87nz3m8eHXVLaUgOoZIqHilRcSYlz+0sf8/z8Am4+pxs3nNU17JLSmhpAFVA8VKT83J1fTF/E1Pc38IOzuvLDwd3CLintqQFUkT7tGnP/cMVDRcrC3bnrlSU8M2c93z2zCz/+1gma278aqAFUofN6fREP/d0bioeKHIm785vXljLx3bVce3pnbh3aQwf/aqIUUBW77hudWbttL4++HZk9VPFQkS+4O797YzmPv7OGa77ekTsuOFEH/2qkBlDFzIy7LurFhh37+bnioSJfct+bK3hk1iquGNCBuy7qpYN/NdMpoGrweTy0heKhIlEPzFjJA2/lc1luO+4e1lsH/xCoAVSTBnVqMn6U4qEiAA/PyuePb67gklPa8r+X9OG443TwD0NCDcDMfmhmi8xssZndHIw1NbM3zWxl8L1JMG5m9oCZ5ZvZQjPrWxkbkEqi8dBtew4qHioZ6/HZq/ndP5Zz0Ult+P2lJ5Glg39oKtwAzKw3MBboD5wEXGBm3YBbgRnu3g2YEdwHGAp0C77GAY8kUHfK6tOuMX8afrLioZKRnvzPGu55bSnf/lpr/niZDv5hS+QdwInAHHff5+6HgLeB/wKGAZOCZSYBFwe3hwFPecQcoLGZtU5g/SnrvF6tuP18zR4qmeXpOeu465UlnNerJX8afjI1snQGOmyJ7IFFwJlm1szMsoHzgfZAS3ffDBB8bxEs3xbYEPP8gmDsS8xsnJnlmVleUVFRAuUltzFndObKAR14ZNYqpr2/PuxyRKrUtPfXc8dLizjnxBb8eURfaurgnxQqvBfcfSnwW+BN4B/AR8ChYzzlSO/1vnL+w90fc/dcd8/NyUnf631G46HfPCGHn7+0iH+v3Bp2SSJV4vn5Bdz24scM6p7DQ1f21UXck0hCe8Ldx7t7X3c/E9gOrAS2RE/tBN8Lg8ULiLxDiGoHbEpk/amuRtZxPBiNhz4znxWKh0qaeenDjfzk+Y84o2tzHr3qVGrXyAq7JImRaAqoRfC9A3AJMBWYDowMFhkJvBzcng5cE6SBBgK7oqeKMtnn8dBaWYx+UvFQSR+vfLSJHz23gIGdm/HY1bnUqamDf7JJ9L3Y38xsCfAKcIO77wDuBc41s5XAucF9gNeA1UA+8DhwfYLrThufx0P3HuC6p/LYf1DxUEltr3+8mZufXUBux6aMH5VL3Vo6+Ccjc0/eGGJubq7n5eWFXUa1eWPxJ3zvmfkM6dWKh67oqz+OkZT0z8WfcP3kDzipfWMmXduf+rU140x1M7P57p5b2nL6NCaJROOhry/S7KGSmt5atoUbpnxA77aNmDi6nw7+SU57J8mMOaMza7Zq9lBJPbNXFPG9pz+gR6uGTLq2Pw3q1Ay7JCmFGkCS0eyhkor+k7+VsU/lcXyL+jw9pj+N6urgnwp0CigJfWn2UMVDJcnNWb2NMZPm0alZPSZfN4DG2bXCLknKSA0gSSkeKqkgb+12rp04j3ZNspk8dgBN6+ngn0rUAJJYNB66fe9BxUMl6cxft4ORE96nVcM6TLluAM3r1w67JCknNYAkF7m4/Mks1OyhkkQ+2rCTURPep3mD2kwZO5AWDeuEXZJUgBpACviW4qGSRBZt3MXV4+fSuF5Npo4dSKtGOvinKqWAUsSYM764uHzHZtmMUDxUQrB086dcNX4uDerUZMp1A2nTuG7YJUkC1ABShJnxywt7sWF7NB5al290S9/ZUiX5rNiymyufmEvdmllMHTuQ9k2zwy5JEqRTQCkkOntotxb1uf6ZDxQPlWqTX7iHKx6fS43jjCljB9KhmQ7+6UANIMUoHirVbc3WvVzx+BwApowdSOfm9UKuSCqLGkAKUjxUqsv6bfu44vE5HCpxpowdQNcW9cMuSSqRGkCKUjxUqtqG7fsY8fgc9hcfZvJ1AzihZYOwS5JKpgaQwmLjob99Y1nY5Uga2bhzP1c8MYfdnxXzzJgBnNi6YdglSRVQCijFReOhf3l7NZ2a1VM8VBL2ya7PuOLxOezcV8zk6wbQu22jsEuSKqIGkOIUD5XKVPhp5OC/bc9Bnh7Tnz7tGoddklQhnQJKA/Hx0OWfKB4q5bd1zwGueGIun3z6GRNH9+OUDk3CLkmqmBpAmmhQpyYTRvWjbq0srp04j8Ldn4VdkqSQ7XsPcuXjcynYsY8nR/Ujt1PTsEuSaqAGkEbaNK7L+JH92L73IGMnKR4qZbNz30GufGIua7ftZcLIfgzo0izskqSaqAGkma+1axSJh27cxS3PKh4qx7ZrfzFXjZ/LqsI9PH5NLqd11dXnMokaQBqKxkP/sfgTfvsPxUPlyD79rJhrxs9l+Se7efTqvpx5gsIDmUYpoDQ15ozOrNu2j7/MXk3HZvW4YoDiofKFPQcOMWrC+yze9CmPXnUqZ/doGXZJEoKE3gGY2S1mttjMFpnZVDOrY2adzWyuma00s2fNrFawbO3gfn7weKfK2AA5MjPjzgt7Mqh7Dne8vIh3VhaFXZIkiX0HD3Htk/P4qGAXD15xCuf01ME/U1W4AZhZW+AmINfdewNZwHDgt8B97t4N2AGMCZ4yBtjh7l2B+4LlpArVyDqOP4/Q7KHyhf0HD3PtxHnkrdvO/cNPZkjv1mGXJCFK9DOAGkBdM6sBZAObgbOB54PHJwEXB7eHBfcJHh9sZpbg+qUUsfFQzR6a2T4rPszYp/KYu2Y7f7zsZC7o0ybskiRkFW4A7r4R+AOwnsiBfxcwH9jp7oeCxQqAtsHttsCG4LmHguWVN6sGsfHQ6ybNUzw0Ax04dJjvPj2f/6zayu+/cxIXn9K29CdJ2kvkFFATIq/qOwNtgHrA0CMsGs0hHunV/lcyimY2zszyzCyvqEjnrSuL4qGZ6+ChEq5/5gPeXlHEvZd8je+c2i7skiRJJHIK6BxgjbsXuXsx8AJwGtA4OCUE0A7YFNwuANoDBI83ArbH/1B3f8zdc909NydHsbTKpHho5ik+XMKNUz9gxrJC7r64N5f3UxpMvpBIA1gPDDSz7OBc/mBgCTAT+E6wzEjg5eD29OA+weNvubtehlazMWd05uqBHfnL7NVMmbs+7HKkCh06XMLN0xbwxuIt/PLCnlw1sGPYJUmSqfDfAbj7XDN7HvgAOAR8CDwGvApMM7O7g7HxwVPGA0+bWT6RV/7DEylcKiYaD92wYx93vByZPVR/AJR+Dpc4P3ruI179eDM///aJjDq9c9glSRKyZH4Rnpub63l5eWGXkZZ2f1bMpY++x8Yd+3n++6fRvZWu9pQuDpc4P/nrR7zw4UZ+OqQH3x90fNglSTUzs/nunlvacpoKIkNp9tD0VFLi3PbCQl74cCM/PvcEHfzlmNQAMphmD00v7s7tLy3iubwCbhrcjRsHdwu7JElyagAZTvHQ9ODu3Dl9MVPfX8/1g47nlnN08JfSqQEI3+rVip9/uyf/WPwJ9yoemnLcnV//fSlPvbeOcWd24SfndUd/ZC9lodlABYBrT+/Eum17eWx25OLymj00Nbg7976+jAn/WcOo0zpx29AeOvhLmakBCBCJh/7igp6s3654aKpwd/7vnyv4y+zVXD2wI3de2FMHfykXnQKSz0UuLt+Xbi3qc8NkXVw+2d0/YyUPzsxnRP/23HVRLx38pdzUAORL6teuwZOjFQ9Ndg/NzOdP/1rJpae2456Lv8Zxx+ngL+WnBiBf0bqR4qHJ7NG3V/H7N5ZzySltuff/9dHBXypMDUCOSPHQ5PTEO6u59/VlXHhSG35/6Ulk6eAvCVADkKOKnT1U8dDwTXp3LXe/upTzv9aK+y7TwV8SpxSQHFP04vKKh4Zr8tx13Dl9Mef2bMn9w0+hRpZeu0ni1ADkmDR7aPiem7eB219cxNk9WvDgFadQUwd/qST6TZJSxcZDr1c8tFr9bX4BP31hIWeekMPDV/aldo2ssEuSNKIGIGVSv3YNJozqR7biodXm5QUb+cnzH3Ha8c147OpTqVNTB3+pXGoAUmZtGtdlwqjoxeUVD61Kry7czC3PLqB/56Y8cU0/HfylSqgBSLn0btuIB0acwscbd3Hzsx8qHloF/rHoE26a9iGndmzC+JGRP8oTqQpqAFJu5/Zsyc+/3ZM3Fm9RPLSS/WvJFm6c+gF92jXiydH9qVdbOQ2pOvrtkgqJnT20Y7NsrhygC44natbyQq6f/AE9Wzdk0rX9qa+Dv1Qx/YZJhcTOHvqLlxfTrkk231Q8tMLeWVnEuKfnc0Kr+jx17QAa1qkZdkmSAXQKSCosfvbQZZ98GnZJKendVVu5blIex+fU5+lrB9AoWwd/qR5qAJKQ6Oyh2bWyGDMxT/HQcpq7ehtjJubRsVk2z4zpT5N6tcIuSTKIGoAkrHUjxUMrIm/tdkZPnEebxnWYfN1AmtWvHXZJkmHUAKRS9G7biD8rHlpmH67fwagn59GyYR2mjh1ITgMd/KX6VbgBmFl3M1sQ8/Wpmd1sZk3N7E0zWxl8bxIsb2b2gJnlm9lCM+tbeZshyeCcni25Q/HQUi0s2Mk1E96nab1aTBk7gBYN64RdkmSoCjcAd1/u7ie7+8nAqcA+4EXgVmCGu3cDZgT3AYYC3YKvccAjiRQuyWn06Z245usdeWz2aibPXRd2OUln0cZdXD3+fRrVrcnUcQNp3ahu2CVJBqusGOhgYJW7rzOzYcCgYHwSMAv4KTAMeMrdHZhjZo3NrLW7b66kGiQJKB76Vdv2HGDW8iLeWl7IzGWFNK5bk6ljB9K2sQ7+Eq7KagDDganB7ZbRg7q7bzazFsF4W2BDzHMKgrEvNQAzG0fkHQIdOmju+VQUjYde+uh73DD5A57//tfp0aph2GVVm5ISZ9GmXcxcFjnoLyzYiTvkNKjNBX1ac+PZ3WjfNDvsMkWwyAvyBH6AWS1gE9DL3beY2U53bxzz+A53b2JmrwL/6+7/DsZnAP/j7vOP9rNzc3M9Ly8vofokPJt37WfYg/+hZtZxvHj9aWl9rnv3Z8X8e+VW3lpWyMzlRWzdcwAzOKldY87u0YKzuregV5uGun6vVAszm+/uuaUtVxnvAIYCH7j7luD+luipHTNrDRQG4wVA+5jntSPSOCRNReOhlz76Htc9lce0cQPJrpUef3zu7qwq2hN5lb+skHlrt3OoxGlYpwZnnpDD2T1a8M0TchTtlKRWGf8bR/DF6R+A6cBI4N7g+8sx4z8ws2nAAGCXzv+nv2iKtm4xAAAHL0lEQVQ8dOzTedzy7AIeufLUlH0V/FnxYd5bvY2ZywqZubyQDdv3A9C9ZQOu+0YXzu7Rgr4dGutyjZIyEjoFZGbZRM7rd3H3XcFYM+A5oAOwHrjU3bebmQEPAkOIJIZGu/sxz+/oFFD6mPDvNfzq70sYd2YXfnb+iWGXU2YFO/Yxc3kRM5cV8u6qrXxWXELdmlmc3rUZg7q34KweLfRhriSdajkF5O77gGZxY9uIpILil3XghkTWJ6lrdIrMHlp8uIQP1u34PLGzYsseADo0zWZ4vw4M6p7DwC7NdIEWSQvpcUJWkp6ZcUeSxkO3BjHNmcsLmb2iiN2fHaJmltG/c1Muy23PoO4tOD6nHpE3sSLpI+EUUFXSKaD0s+fAIS599D02bN8XWjw0GtOMJnZiY5pndY98gHt61+Y00JTMkqLKegpIDUCq3eZd+7n4of+QZcZLN5xeLfHQT2NimrNiYpont2/MWd1bcHaPFvRsrZimpIfqjIGKlEvrRnUZP7Ifl/3lPcZMyuPZ71Z+PNTdyS/cw8zlhby1rJC8tTs+j2l+s3sLzuqeo5imZDw1AAlF77aNeGD4KYx7Oo+bpy3gkatOJSvBV9+xMc23lhVSsCMS0+zRqgFjz+zCWd0V0xSJpQYgoTmnZ0vuuKAnd72yhHtfX8rt3+5Z7p9xrJjm9wcdz6DuimmKHI0agIRq9OmdWbt1L4+/s4aOzepx1cBjx0OLD5cwf92Oz/8YKz6meVaPFgzo3FQxTZEyUAOQ0EXjoXmv/IXv/OtF6hzaDHXbwtA7oc9lFO0+wNsrIq/yZ6/8akzzrB4t6NJcMU2R8lIDkNDVyDqOR/qshiWPUWfKTlh/GDrsoXjbDTyQs5wHt/fFHVo0qM35vVtzVo8cxTRFKoEagCSFOv/6NTy/E9YG1xNee5iaf93B1VdOotY5wzlLMU2RSqcGIMlh/8bIK/9Y6w/TosZWbhzcLZyaRNKc8nCSHOq2hQ5xH9x2yIqMi0iVUAOQ5DD0ThjeDDplRX4rO2VF7g+9M+zKRNKWTgFJcuhzWeR747sip4NiUkAiUjXUACR59LlMB3yRaqRTQCIiGUoNQEQkQ6kBiIhkKDUAEZEMpQYgIpKhkvqKYGZWBKwLu44yag5sDbuIKpTO26dtS13pvH2JbFtHdy/1ottJ3QBSiZnlleUSbKkqnbdP25a60nn7qmPbdApIRCRDqQGIiGQoNYDK81jYBVSxdN4+bVvqSuftq/Jt02cAIiIZSu8AREQylBqAiEiGUgOoBGY2xMyWm1m+md0adj2JMLP2ZjbTzJaa2WIz+2Ew3tTM3jSzlcH3JmHXWlFmlmVmH5rZ34P7nc1sbrBtz5pZrbBrrCgza2xmz5vZsmAffj1d9p2Z3RL8Ti4ys6lmVieV952ZTTCzQjNbFDN2xH1lEQ8Ex5iFZta3MmpQA0iQmWUBDwFDgZ7ACDPrGW5VCTkE/NjdTwQGAjcE23MrMMPduwEzgvup6ofA0pj7vwXuC7ZtBzAmlKoqx/3AP9y9B3ASke1M+X1nZm2Bm4Bcd+8NZAHDSe19NxEYEjd2tH01FOgWfI0DHqmMAtQAEtcfyHf31e5+EJgGDAu5pgpz983u/kFwezeRA0hbIts0KVhsEnBxOBUmxszaAd8GngjuG3A28HywSCpvW0PgTGA8gLsfdPedpMm+I3L9krpmVgPIBjaTwvvO3WcD2+OGj7avhgFPecQcoLGZtU60BjWAxLUFNsTcLwjGUp6ZdQJOAeYCLd19M0SaBNAivMoS8ifgf4CS4H4zYKe7Hwrup/L+6wIUAU8Gp7ieMLN6pMG+c/eNwB+A9UQO/LuA+aTPvos62r6qkuOMGkDi7AhjKZ+tNbP6wN+Am93907DrqQxmdgFQ6O7zY4ePsGiq7r8aQF/gEXc/BdhLCp7uOZLgXPgwoDPQBqhH5LRIvFTdd6Wpkt9TNYDEFQDtY+63AzaFVEulMLOaRA7+k939hWB4S/QtZ/C9MKz6EnA6cJGZrSVyqu5sIu8IGgenFSC1918BUODuc4P7zxNpCOmw784B1rh7kbsXAy8Ap5E++y7qaPuqSo4zagCJmwd0C9IItYh8MDU95JoqLDgnPh5Y6u5/jHloOjAyuD0SeLm6a0uUu9/m7u3cvROR/fSWu18JzAS+EyyWktsG4O6fABvMrHswNBhYQhrsOyKnfgaaWXbwOxrdtrTYdzGOtq+mA9cEaaCBwK7oqaKEuLu+EvwCzgdWAKuA28OuJ8FtOYPIW8uFwILg63wi58pnACuD703DrjXB7RwE/D243QV4H8gH/grUDru+BLbrZCAv2H8vAU3SZd8BdwHLgEXA00DtVN53wFQin2cUE3mFP+Zo+4rIKaCHgmPMx0TSUAnXoKkgREQylE4BiYhkKDUAEZEMpQYgIpKh1ABERDKUGoCISIZSAxARyVBqACIiGer/AyVjtJ9+Yn9TAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cas binomial: Nombre optimal de journaux a commander *49.000000*, Moyenne de la demande *50.000000*\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cas Poisson: Nombre optimal de journaux a commander *48.000000*, Moyenne de la demande *50.000000*\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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iI4Ul5fzjy1QiQh3MHNktoI4TVsqfOJ2G6R9sITLM4ZNtnj1NC0A1PHJNJ04Vl7Pgu33UC3Pw+2u72B1JKVUDS9cdIDntBH+9pRdN6wdGu4eqaAGoBhHh8Ru6Ulhaxstf7SEyNJj7r+xodyyl1AU4mlvE7M92MKRjNLcEULuHqmgBqCYR4ekbe1JYUs5fP99JRIiDuy9tZ3cspVQ1zVyZQkm5k2duDKx2D1XRAnABHEHC327tTWFpOX/+5zYiQx2MHdja7lhKqfNYlXKUz7dm8OjwLgHX7qEqehjoBQp2BDHnjr5c3imGGR9uYcVPh+yOpJSqwsmiUmaudLV7mHqZfmuv7LwFQEQWiEimiKRUGosSkdUistu6bGKNi4jMEZFUEdksIv0qPWaitfxuEZlYO5tTN8KCHbx2V38Gto3ikXc38fnWo3ZHUkqdw+zPArvdQ1Wq86/xJjD8tLHpwBpjTDywxroNMAKIt/6mAa+Cq2AAM4FBwEBgZkXR8FURoQ7mTxpAr7hGPLB0I1/vyrI7klLqNOv3Z7Mk6QCThwRuu4eqnLcAGGO+AbJPGx4NLLSuLwRurDS+yLisBRqLSAvgWmC1MSbbGHMCWM2ZRcXn1A8L5s1JA+nYrD6/XJzM2r3H7Y6klLIUl5Uz/YPNxDaO4JFrArfdQ1Vq+n2ouTHmCIB1WfFzuljgYKXl0q2xc42fQUSmiUiyiCRnZXn/p+pGkSEsnjKQuCaRTHlzPT8dzLE7klIKePmrPezJOsUzAd7uoSqenhA727FVporxMweNmWuMSTDGJMTExHg0XG2Jrh/GkqmDiK4fxoT5SWw7fNLuSEoFtF0Zebz671RG92nJFQHe7qEqNS0AGdbUDtZlpjWeDrSqtFwccLiKcb/RvGE4S6YOol5YMOPnJ5GamWd3JKUCktNpmLF8C/XCgnn8Bm33UJWaFoCVQMWRPBOBFZXGJ1hHAw0Gcq0pos+BX4hIE2vn7y+sMb/SKiqSJVMHISKMS0ziwPECuyMpFXCWrDvAhrQT/On6btru4TyqcxjoMuAHoLOIpIvIFGAWcI2I7AausW4DfArsBVKBecB9AMaYbOAvwHrr78/WmN9pH1Oft6YOpLjMyZ2JazmcU2h3JKUCRkW7h0s7NuXmfmfdzagqEWO8t899QkKCSU5OtjtGjWxOz2HcvCRiGoTxzi8vJqaBfhJRqrZNW5TM17uy+OLhobSJDtxf/IrIBmNMwvmW019F1JJecY1ZMHkAR3KLGD8/iZyCErsjKeXXVqUc4YttGTx8TaeAfvO/EFoAatGAtlHMm5DA3mOnmLhgHXlFpXZHUsov5RaW8sSKrXRr0ZCp2qSx2rQA1LJL45vyyp392Hr4JFPeTKagpMzuSEr5ndmrdnAsv5hZN/ckWNs9VJv+S9WBq7s158Xb+5Ccls0vF2+guKzc7khK+Y31+7NZarV76BWn7R4uhBaAOjKyd0tm39yL/+w+xv1LNlJa7rQ7klI+T9s9uEcLQB26NaEVfx7dnX9tz+CRdzdR7vTeI7CU8gXa7sE9+i9WxyZc3JaCknJmfbaDiJAgZo3pRVCQnp1IqQtV0e7hRm33UGNaAGxw7+UdKCgpZ86a3USEOHhyVHc9RZ1SF6Ci3UN9bffgFi0ANnn46ngKistI/HYfEaHBPDq8sxYBpappSVIaG9JO8MKtvYnWdg81pgXAJiLCY9d3pbC0nNe+3kO9UAcPDIu3O5ZSXu9IbiGzV+3ksvimjNF2D27RAmAjEeEvo3tQWFLOC6t3ERHqYOpl7e2OpZTXMsbwxIqtlDmdPHNjT/3W7CYtADYLChKev6UXhaXlPP3JdiJDg7lzUGu7YynllValHGX1tgxmjOhC6+hIu+P4PD0M1AsEO4L4+9i+XNk5hsc+2sKHG9PtjqSU18ktLGXmSle7hyna7sEjtAB4idDgIF69qz+D20Xzu/c2syrliN2RlPIqsz5ztXuYfXMvbffgIfqv6EXCQxwkTkygd1wjHli2ka92Zp7/QUoFgKS9x1m27gB3D2lHz7hGdsfxG1oAvEy9sGDemDyQTs0bcO/iDfyw57jdkZSyVVFpOTM+3EJckwge+YW2e/AkLQBeqFFECIunDKJ1VCRTFq7nxwMn7I6klG1e+SqVvVmneOamnkSG6nErnqQFwEtF1QtlydRBNGsQxsQF60g5lGt3JKXq3K6MPF79eg839mnJ5Z1i7I7jd7QAeLFmDcNZcs9gGoaHMGHBOnZn5NkdSak643Qapn+wWds91CK3CoCIPCgiKSKyVUQessaiRGS1iOy2LptY4yIic0QkVUQ2i0g/T2yAv4ttHMGSqYNwBAnjEpPYf+yU3ZGUqhNvJaXx44EcHr+hm7Z7qCU1LgAi0gO4BxgI9AZuEJF4YDqwxhgTD6yxbgOMAOKtv2nAq27kDihtm9ZjydRBlJY7GZeYxKGcQrsjKVWrjuQW8rzV7uGmvtruoba48w2gK7DWGFNgjCkDvgZuAkYDC61lFgI3WtdHA4uMy1qgsYi0cGP9AaVT8wYsnjKIk4Wl3JWYRGZekd2RlKoVxhge/yhF2z3UAXcKQAowVESiRSQSuA5oBTQ3xhwBsC4rGnXHAgcrPT7dGlPV1CO2EW/ePYCMk0XclZhE9qkSuyMp5XGfbjnKv7Zn8sg1nbTdQy2rcQEwxmwHZgOrgVXAJqCqM56frYyfcUosEZkmIskikpyVlVXTeH6rf5soEicksP94ARMXrONkUandkZTymNwCV7uHHrENuXuItnuobW7tBDbGzDfG9DPGDAWygd1ARsXUjnVZ8XPWdFzfECrEAYfP8pxzjTEJxpiEmBg97OtsLunYlNfu6seOoyeZ/MZ6CkqqqrtK+Y7nPtvOiYISZo3Rdg91wd2jgJpZl62BMcAyYCUw0VpkIrDCur4SmGAdDTQYyK2YKlIX7qouzfn72L5sPHCCexYlU1Rabnckpdyydu9x3l5/kCmXtqNHrLZ7qAvultgPRGQb8DFwvzHmBDALuEZEdgPXWLcBPgX2AqnAPOA+N9cd8K7r2YK/3dqb71KPc/+SHyktd9odSakaKSot54/Lt9AqKoKHr9Z2D3XFrd9VG2MuO8vYcWDYWcYNcL8761NnGtMvjoKScv70UQoPvfMTc8b2xaEnmVc+5qUvU9l77BSLpwwkItRhd5yAoY01/MBdg9tQWFLOM59uJyLEwfM39yJIi4DyETuOnuS1r/cwpm8sl8Xrfr+6pAXAT9wztD0FJeW8+K9dRIQ4+PPo7nr8tPJ65U7DjOVbaBgRwp+03UOd0wLgR34zrCMFJWW8/s1eIkMdTB/RRYuA8mqLf9jPxgM5vHh7b6LqhdodJ+BoAfAjIsL0EV0oKCm3ikAwD14db3cspc7qcE4hf/18J0M7xXBjH/1NqB20APgZEeGpUd0pLHVNB0WGOrhnaHu7Yyn1PyraPTgNPHNjD/2mahMtAH4oKEiYfXMvCktdO4bDQx2MH9zG7lhK/eyTLUdYsyOTP13flVZR2u7BLloA/JQjSHjxtj4UlZTz+EcpRIY4uLl/nN2xlCKnoIQnV26lZ2wjJl3S1u44AU1/a+3HQoODeHlcP4Z0jOb372/i0y36w2tlv2c/3c6JglJm3dxT2z3YTP/1/Vx4iIN5ExLo17oJv1m2kS93ZNgdSQWw7/cc493kdO65rD3dW2q7B7tpAQgAkaHBLJg8gK4tGnLvWz/yfeoxuyOpAFTR7qFNdCQP6dFpXkELQIBoGB7CorsH0i66HlMXJbMhLdvuSCrAzFmzm/3HC3j2pp6Eh2i7B2+gBSCANKkXyuKpA2neMJxJC9aTcijX7kgqQGw7fJK53+zllv5xDOnY1O44yqIFIMA0axDOkqmDaBgRwvj5Sew8mmd3JOXnXO0eNtM4MoTHrutqdxxViRaAANSycQRL7xlEiCOIu+Ynse/YKbsjKT/25vf72ZSeyxMju9NE2z14FS0AAapNdD2WTB1EudMwbt5a0k8U2B1J+aH0EwW88MVOruwcw8heLeyOo06jBSCAxTdvwKK7B5JXXMa4xCQyTxbZHUn5EWMMj32YAsBftN2DV9ICEOB6xDbizckDycorZlxiEtmnSuyOpPzEyk2H+XpXFr+/tjNxTbTdgzfSAqDo36YJ8ycO4EB2AePnJ5FbWGp3JOXjsk+V8NTH2+jTqjETLm5rdxx1DloAFAAXd4jm9fH92ZWRx+Q31nGquMzuSMqHPf3JNk4WljL75l56ilIvpgVA/eyKzs34xx392JSey9SFyRSVltsdSfmgb3ZlsfzHQ/zqig50vqiB3XFUFdwqACLysIhsFZEUEVkmIuEi0k5EkkRkt4i8IyKh1rJh1u1U6/62ntgA5VnDe1zE327txdp9x/nVWxsoKXPaHUn5kIKSMv744Rbax9Tj/is72h1HnUeNC4CIxAK/ARKMMT0ABzAWmA28aIyJB04AU6yHTAFOGGM6Ai9ayykvdFPfOJ69qSdf7cziwbc3UlauRUBVz/99sYv0E4XMGtNL2z34AHengIKBCBEJBiKBI8BVwPvW/QuBG63ro63bWPcPEz0uzGvdMbA1j9/Qjc9SjvKH9zfjdBq7Iykvt+lgDgu+28edg1ozsF2U3XFUNdT4hDDGmEMi8jfgAFAIfAFsAHKMMRV7ENOBipN9xgIHrceWiUguEA1oa0ovNeXSdhQUl/HC6l1EhDp4Wo/lVudQWu7k0Q8207R+GNNHdLE7jqqmGhcAEWmC61N9OyAHeA8YcZZFKz46nu2d44yPlSIyDZgG0Lp165rGUx7y66s6cqqknNe+3kNkqIM/XtdVi4A6w9xv9rLjaB6vj+9Pw/AQu+OoanLnlJBXA/uMMVkAIrIcuARoLCLB1reAOOCwtXw60ApIt6aMGgFn9CQ2xswF5gIkJCTovIPNRIRHh3emsKSMef/ZR0RoMI9c08nuWMqL7M3K5+9rdjOix0Vc2/0iu+OoC+DOPoADwGARibTm8ocB24CvgFusZSYCK6zrK63bWPd/aYzRN3gfICLMHNmdW/vHMWfNbl77eo/dkZSXcDoNM5ZvITw4iKdGdbc7jrpA7uwDSBKR94EfgTJgI65P7p8Ab4vI09bYfOsh84HFIpKK65P/WHeCq7oVFCTMurkXRWVOZn22g8hQh/7CU/FO8kGS9mUz++aeNGsYbnccdYHcmQLCGDMTmHna8F5g4FmWLQJudWd9yl6OIOH/butNYUk5T6zYSniIg9sSWtkdS9kk42QRz366nYvbR+t/Bz5KfwmsLkiII4iX7uzLZfFNmf7BZj7edPj8D1J+xxjD4x+lUFLm5LkxPfXAAB+lBUBdsPAQB3PHJ5DQJoqH3/mJf23LsDuSqmOrUo7yxbYMHr6mE22b1rM7jqohLQCqRiJCHcyflEC3lg25b8mPfLtbf84RKHILSnli5Va6t2zI1Evb2R1HuUELgKqxBuEhLLp7IO1j6nHPomSS959xVK/yQ898uo3sUyXMvrkXwQ59C/Fl+uoptzSODGXxlEG0aBTO5DfWszk9x+5IqhZ9u/sY7yanM21oe3rENrI7jnKTFgDltpgGYSy5ZxCNIkOYsGAdO4/m2R1J1YKCkjJmfLiZdk3r8eCweLvjKA/QAqA8okWjCJZOHUxYcBDjEpPYm5VvdyTlYS98sYuD2YXMGtNTO336CS0AymNaR0eyZOpgjDGMS0ziYHaB3ZGUh2w8cII3vtvHuEGtGdQ+2u44ykO0ACiP6tisPounDKKgpJxxiUkczS2yO5JyU3FZOY9+sJnmDcO106ef0QKgPK5by4YsvHsgx/OLGZe4luP5xXZHUm545as97MrI59mbetJAO336FS0Aqlb0adWYBZMGcCinkPHz15FbUGp3JFUDO46e5OWvUrmpbyxXdmlmdxzlYVoAVK0Z1D6a18cnkJqZz8Q31pFfXHb+BymvUVbu5NH3N9MoIoTHb+hmdxxVC7QAqFp1eacY/nFnX7YcymXKm+spLCm3O5Kqpvnf7mNTei5Pje5OVL1Qu+OoWqAFQNW6a7tfxP/d1pt1+7O5960NFJdpEfB2e7LyeWH1Lq7t3pzre7awO46qJVoAVJ0Y3SeWWWN68vWuLH6zbCOl5U7i9kJ6AAAPwUlEQVS7I6lzcDoNj76/mYgQB38ZreeB9mdaAFSduX1Aa54c2Y3Pt2bwu/c2Ue7UE8J5o0U/7Cc57QSP39BNT/Li59w6IYxSF2rSkHYUlJbz/KqdRIQ4tJe8lzlwvIDZq3ZyeacYbu4Xa3ccVcu0AKg6d98VHSkoLuelr1IJD3Ewc2Q3LQJewOk0/OGDTQQHiRbmAKEFQNnit7/oREFJOQu+20e9MAe/v1Z/YWq3JUlprN2bzawxPWnZOMLuOKoOaAFQthARHr+hKwUlZbz81R4iQ4O5/8qOdscKWAezC3jusx1cFt+U2wfo+X0DRY13AotIZxH5qdLfSRF5SESiRGS1iOy2LptYy4uIzBGRVBHZLCL9PLcZyheJCM/c1JPRfVry1893suDbfXZHCkhOp+EP728mSHTqJ9DUuAAYY3YaY/oYY/oA/YEC4ENgOrDGGBMPrLFuA4wA4q2/acCr7gRX/sERJLxwa2+u7d6cP/9zG2+vO2B3pIDzVlIaP+w9zp+u70pck0i746g65KnDQIcBe4wxacBoYKE1vhC40bo+GlhkXNYCjUVEf2GiCHYEMeeOvlzeKYYZH27ho42H7I4UMNKOn+K5T3cwtFOMTv0EIE8VgLHAMut6c2PMEQDrsqKDVCxwsNJj0q0xpQgLdvD6+P4MbhfNb9/bxKqUI3ZH8ntOp+H3720m2CHMvlmnfgKR2wVAREKBUcB751v0LGNn/BJIRKaJSLKIJGdlZbkbT/mQ8BAHiRMT6B3XiAeWbeSrnZl2R/JrC77bx7r92Tx+QzdaNNKjfgKRJ74BjAB+NMZkWLczKqZ2rMuK/4vTgcrfMeOAw6c/mTFmrjEmwRiTEBMT44F4ypfUCwvmjckD6XxRA+5dvIHvU4/ZHckv7c7I4/nPd3J11+bc2j/O7jjKJp4oAHfw3+kfgJXAROv6RGBFpfEJ1tFAg4HciqkipSprFBHCorsH0SY6kqmLktmQlm13JL9SWu7kkXc3UT8sWI/6CXBuFQARiQSuAZZXGp4FXCMiu637ZlnjnwJ7gVRgHnCfO+tW/i2qXihvTR1E84bhTFqwns3pOXZH8hsvf5XKlkO5PHNjD2IahNkdR9nIrQJgjCkwxkQbY3IrjR03xgwzxsRbl9nWuDHG3G+M6WCM6WmMSXY3vPJvzRqEs2TqIBpFhjB+/jq2HzlpdySf99PBHP7xpesMXyO0zXPA026gyqu1bBzBsnsGExHi4K7EJFIz8+2O5LNOFZfx0NsbuahhOE+O6m53HOUFtAAor9cqKpIl9wxCRLhz3lr2HztldySf9PQn20nLLuCF23rTKEJP7q60ACgf0SGmPkumDqK03Mm4xCTSTxTYHcmn/GtbBsvWHeCXQzswuH203XGUl9ACoHxG54sasHjKIPKKSrlzXhJHcgvtjuQTMk4W8fv3N9GtRUMeuaaT3XGUF9ECoHxKj9hGLJoyiOxTJYybl0RmXpHdkbya02l45N2fKCp1MueOvoQG6//y6r/0vwblc/q0aszCuwdw9GQR4+YlcTy/2O5IXuv1b/byXepxnhzVjY7N6tsdR3kZLQDKJ/VvE8WCSQM4eKKAcYlJZJ8qsTuS19l44AQvfLGT63u24LYEbfSmzqQFQPmswe2jmT9xAPuOneKuxCRyCrQIVMgpKOHXSzfSvGE4z+qvfdU5aAFQPm1Ix6bMnZBAamY+4+evI7eg1O5ItjPG8Lv3NpOZV8TL4/rpIZ/qnLQAKJ93eacYXh/fn51H8xi/IIncwsAuAvO/3ce/tmcwY0RX+rRqbHcc5cW0ACi/cGWXZrw2vh/bj5xk/PzALQIb0rKZ9dkOru3enMlD2todR3k5LQDKb1zVpTmv3dX/v0UgwKaDMk8Wce9bPxLXJILnb+mt8/7qvLQAKL8yrKurCOw4kse4+WsDZsdwSZmT+5b8SH5RGa+PT9B5f1UtWgCU3xnWtTmvj+/Prox87pwXGIeIPv3JNpLTTvD8Lb3ofFEDu+MoH6EFQPmlK7s0Y96EBPZk5TN27g9+/Yvht9amseiHNO65rB0je7e0O47yIVoAlN+6vFMMb0waQPqJQm5/fS2Hc/yvd9C3u48xc+VWruwcw/QRXe2Oo3yMFgDl1y7p2JTFUwZyLK+YW1/7wa9aSe/Jyue+JRvoGFOfOXf0xRGkO33VhdECoPxe/zZRLL1nMAUlZdzy2g9sO+z7ZxbLyitm8hvrCXEEkTgxgQbhutNXXTgtACog9IxrxHv3XkKIQ7h97g+s2+e7J5rPKypl0hvryMorJnFiAq2iIu2OpHyUFgAVMDo2q8/7v7qEmAZhjJ+fxKqUo3ZHumDFZeX8cvEGdh7N49W7+tG3dRO7Iykf5lYBEJHGIvK+iOwQke0icrGIRInIahHZbV02sZYVEZkjIqkisllE+nlmE5SqvtjGEbz3y4vp1rIhv1qygTe+22d3pGorKXPy66Ub+X7PcZ6/pRdXdG5mdyTl49z9BvB3YJUxpgvQG9gOTAfWGGPigTXWbYARQLz1Nw141c11K1Uj0fXDWDp1MNd0bc5TH2/jzx9vo6zcaXesKpWWO/n10h9ZvS2DP4/uzph+cXZHUn6gxgVARBoCQ4H5AMaYEmNMDjAaWGgtthC40bo+GlhkXNYCjUWkRY2TK+WGiFAHr97Vn8lD2rLgu33cvTDZa/sHlZQ5eWDpRr7YlsFTo7oz4eK2dkdSfsKdbwDtgSzgDRHZKCKJIlIPaG6MOQJgXVZ8T40FDlZ6fLo1ppQtHEHCzJHdeW5MT37Yc4ybXv6O1Mx8u2P9j/ziMqYsXM+qrUeZObIbEy9pa3ck5UfcKQDBQD/gVWNMX+AU/53uOZuzHaRszlhIZJqIJItIclZWlhvxlKqeOwa2ZsnUweQUljLqpW9Z8dMhuyMBrkM9x879ge/3HOevt/Ri8pB2dkdSfsadApAOpBtjkqzb7+MqCBkVUzvWZWal5Sufly4OOHz6kxpj5hpjEowxCTExMW7EU6r6BraL4pPfXEq3Fg158O2fmLF8C4Ul5bbl2Xo4lzGvfseezFMkTkjgVj2lo6oFNS4AxpijwEER6WwNDQO2ASuBidbYRGCFdX0lMME6GmgwkFsxVaSUN2jRKIJl0wZz7+UdWLbuANfN+Q8b0ur+9wLvJR9kzCvfU1pmWDZtMFd20aN9VO0QY86Yhan+g0X6AIlAKLAXmIyrqLwLtAYOALcaY7LF1Zz8JWA4UABMNsYkV/X8CQkJJjm5ykWUqhXfpx7j9+9v5nBuIVMvbceDV3eiflhwra4zt7CUv/xzG+9vSOeSDtHMuaMvTeuH1eo6lX8SkQ3GmITzLudOAahtWgCUnfKLy3j20+0sTTpAswZh/GF4F8b0jSWoFnrurEo5wuMrtpJ9qoRfXd6Bh66OJ9ihv9NUNaMFQCkP+fHACZ76eBubDubQvWVD7ruiI8N7XOSR5ms/HjjBi6t38Z/dx+jWoiHP39KLHrGNPJBaBTItAEp5kNNp+OinQ/zjy1T2HTtF2+hI7hrchpG9W9K8Yfj/Lrz5XfjsKSg8BBGxMGIm9Lrt57tLypx8vSuLt9am8fWuLKLrhfKrKzow8ZK2hOinfuUBWgCUqgXlTsMXW4/y2jd72XQwBxEY1C6KIR2a0rd1E/rlrCZi+UPI28fhQDm0dmDGRpNx3V/5LvIqktOy+SzlKDkFpTStH8rUy9oz4eI2RIbW7v4FFVi0AChVy/Zk5fPxpsN8tuUoOzPyAPiWB4h75wDsr3QIaVsH6be35lL+Qf2wYK7s0oyb+rbksvgY/cSvakV1C4B+7FCqhjrE1Oehqzvx0NWdyC0sZXN6DrFvZbs++Vd2oJzYsGxW3zeU9jH19cQtymvoxw+lPKBRRAiXxccgkbHQ2vG/d7Z2IJGxxDdvoG/+yqtoAVDKk0bMhLHR0Nbh+r+rrcN1e8RMu5MpdQadAlLKkyqO9ml87qOAlPIWWgCU8rRet+kbvvIJOgWklFIBSguAUkoFKC0ASikVoLQAKKVUgNICoJRSAcqrW0GISBaQZneOamoKHLM7RC3y5+3TbfNd/rx97mxbG2PMeU+p6NUFwJeISHJ1em/4Kn/ePt023+XP21cX26ZTQEopFaC0ACilVIDSAuA5c+0OUMv8eft023yXP29frW+b7gNQSqkApd8AlFIqQGkBUEqpAKUFwANEZLiI7BSRVBGZbnced4hIKxH5SkS2i8hWEXnQGo8SkdUistu6bGJ31poSEYeIbBSRf1q324lIkrVt74hIqN0Za0pEGovI+yKyw3oNL/aX105EHrb+m0wRkWUiEu7Lr52ILBCRTBFJqTR21tdKXOZY7zGbRaSfJzJoAXCTiDiAl4ERQDfgDhHpZm8qt5QBvzXGdAUGA/db2zMdWGOMiQfWWLd91YPA9kq3ZwMvWtt2AphiSyrP+DuwyhjTBeiNazt9/rUTkVjgN0CCMaYH4ADG4tuv3ZvA8NPGzvVajQDirb9pwKueCKAFwH0DgVRjzF5jTAnwNjDa5kw1Zow5Yoz50bqeh+sNJBbXNi20FlsI3GhPQveISBxwPZBo3RbgKuB9axFf3raGwFBgPoAxpsQYk4OfvHa4zl8SISLBQCRwBB9+7Ywx3wDZpw2f67UaDSwyLmuBxiLSwt0MWgDcFwscrHQ73RrzeSLSFugLJAHNjTFHwFUkgGb2JXPL/wP+ADit29FAjjGmzLrty69feyALeMOa4koUkXr4wWtnjDkE/A04gOuNPxfYgP+8dhXO9VrVyvuMFgD3ne0s3z5/bK2I1Ac+AB4yxpy0O48niMgNQKYxZkPl4bMs6quvXzDQD3jVGNMXOIUPTvecjTUXPhpoB7QE6uGaFjmdr75251Mr/51qAXBfOtCq0u044LBNWTxCREJwvfkvMcYst4YzKr5yWpeZduVzwxBglIjsxzVVdxWubwSNrWkF8O3XLx1IN8YkWbffx1UQ/OG1uxrYZ4zJMsaUAsuBS/Cf167CuV6rWnmf0QLgvvVAvHU0QiiuHVMrbc5UY9ac+HxguzHm/yrdtRKYaF2fCKyo62zuMsbMMMbEGWPa4nqdvjTGjAO+Am6xFvPJbQMwxhwFDopIZ2toGLANP3jtcE39DBaRSOu/0Ypt84vXrpJzvVYrgQnW0UCDgdyKqSK3GGP0z80/4DpgF7AHeMzuPG5uy6W4vlpuBn6y/q7DNVe+BthtXUbZndXN7bwC+Kd1vT2wDkgF3gPC7M7nxnb1AZKt1+8joIm/vHbAU8AOIAVYDIT58msHLMO1P6MU1yf8Ked6rXBNAb1svcdswXU0lNsZtBWEUkoFKJ0CUkqpAKUFQCmlApQWAKWUClBaAJRSKkBpAVBKqQClBUAppQKUFgCllApQ/x/mjtYrJUxZlAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c=10;cm=20;cs=5;cf=200;\n",
    "\n",
    "# la fonction coût j(u,w)\n",
    "def jj(u,w):\n",
    "    # A vous : écrire la fonction j (voir slides)\n",
    "\n",
    "\n",
    "def J(u,pi,wi):\n",
    "    # A vous : écrire la fonction J = la moyenne de j (voir slides)\n",
    "\n",
    "\n",
    "def resultats(pi,wi,dessin='oui'):\n",
    "# draw the function and the minimum \n",
    "\n",
    "    # remplir val avec les valeurs de J(u) quand u varie de -10 a 100 avec un pas de 1\n",
    "    u=np.linspace(-10,100,num=111)\n",
    "    val=np.zeros(u.size);\n",
    "    for i in range(0,u.size):\n",
    "        # A vous : val[i]= ??\n",
    "        # val[i]=  # modifier\n",
    "    \n",
    "    # recherche du min \n",
    "    # A vous : trouver la valeur uopt\n",
    "    # uopt = ?\n",
    "    \n",
    "    if dessin=='oui':\n",
    "        plt.plot(u,val);\n",
    "        plt.title(\"fonction coût\");\n",
    "        plt.plot(uopt,val[imin],marker='o',markerfacecolor='r')\n",
    "\n",
    "        print(\"Nombre optimal de journaux a commander *%f*, \" % uopt,end='');\n",
    "        print(\"Moyenne de la demande *%f*\\n\" % sum(wi*pi));\n",
    "\n",
    "    return uopt\n",
    "\n",
    "\n",
    "pi, wi, W, title = choisir_loi(discrete) # poisson, binomiale, discrete\n",
    "print('Cas discrêt: ',end='')\n",
    "resultats(pi,wi)\n",
    "plt.show()\n",
    "    \n",
    "pi, wi, W, title = choisir_loi(binomiale) # poisson, binomiale, discrete\n",
    "print('Cas binomial: ',end='')\n",
    "resultats(pi,wi)\n",
    "plt.show()\n",
    "\n",
    "pi, wi, W, title = choisir_loi(poisson) # poisson, binomiale, discrete\n",
    "print('Cas Poisson: ',end='')\n",
    "resultats(pi,wi)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Question 3.__ Vérifier sur un graphique que le nombre de journaux optimal à commander s’obtient par la formule :\n",
    "\n",
    "$$\\text{uopt} = \\inf\\left\\{z ∈ ℝ |F (z) ≥ (c_M − c)∕ (c_M + c_S )\\right\\}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc6d8eb0da0>]"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pi, wi, W, title = choisir_loi(binomiale) # poisson, binomiale, discrete\n",
    "\n",
    "# On dessine F \n",
    "fstar = (cm-c)/(cm+cs) # valeur limite\n",
    "Fv= np.cumsum(pi) # calcul de la fonction de repartition\n",
    "plt.clf()\n",
    "xx=np.hstack((0,wi)) # on rajoute 0 a wi\n",
    "yy=np.hstack((0,Fv)) # on rajoute 0 a Fv\n",
    "plt.step(xx,yy,where='post') # tracé de la fonction de répartition\n",
    "plt.plot(xx,fstar*np.ones(xx.size)) # droite horizontale de valeur fstar\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# chercher l'indice qui donne uopt avec la formule du cours\n",
    "kopt=0\n",
    "for i in range(0,Fv.size):\n",
    "    if Fv[i] >= fstar:\n",
    "        kopt=i\n",
    "        break;\n",
    "\n",
    "plt.step(xx,yy,where='post') # marker='o',markerfacecolor='r');\n",
    "plt.plot(xx,fstar*np.ones(xx.size))\n",
    "plt.plot(wi[kopt],Fv[kopt],marker='o',markeredgewidth=5,markeredgecolor='r',markerfacecolor='r');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Paragraphe 1.3._ On utilise maintenant une loi discrète à 3 valeurs (law=2)\n",
    "\n",
    "Dans le cas précédent, on trouve que le nombre de journaux optimal à commander est très voisin de la moyenne de la demande. On cherche ici à construire un exemple ou les deux nombres seront franchement différents."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Question 4.__ Reprendre ce qui précède, en vous plaçant maintenant dans le cas 2 et chercher à caler des valeurs des probabilités qui permettent d’obtenir le résultat souhaité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre optimal de journaux a commander *10.000000*, Moyenne de la demande *23.750000*\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "wi=np.array([10,50,80])\n",
    "pi=np.array([3/4,1/8,1/8])\n",
    "\n",
    "resultats(pi,wi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Paragraphe 1.4_ La loi du coût\n",
    "\n",
    "__Question 5.__ Dans les cas 1 (binomiale) et cas 2 (discrete), faites un graphique de la loi du coût pour diverses valeurs de la commande $u$. On procédera de deux façons différentes\n",
    "    - En calculant la loi du coût.\n",
    "    - En approchant la loi du coût au moyen de tirages de la demande (loi empirique des coûts)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "52\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 51 artists>"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AB6uquvLd3dU9W4BLgX+eTNMlScu15JF+d45+L/AAsAG4s6oOJbkZmKuqWeAO4O7ui9rjDN4Y6Ordy+BL3xPAL3rljiRNT69pGKrqAHBgpOzGoeUXgGsX2ff3gN9bRRtPl6meXjpNWugjtNHPFvoIbfTztPYxg7MwkqQWOA2DJDWkmdBPciTJE0keSzLXlb06yUeSfLr7+aquPEn+tJs+4vEkr5tu6/tbpJ83JfmPruyxJD8xVH/NTZOR5Nwk9yX5VJInk/zAOh3Lcf1cN2OZ5LuH+vFYkv9O8kvraSxfoY/TG8eqauIBHAHOHyn7fWBft7wPuLVb/gngwwzuM3gj8PC027/Kft4E/OqYuluBTwBnAVuAp4AN0+5Djz7eBfx8t7wJOHedjuW4fq6rsRxq/wbgPxlca77uxnJMH6c2js0c6S9iF4M/LLqfbxkqf38NfAw4N8lrptHAU+yr02RU1b8BJ6fJOGMl+RbgCgZXjFFVL1bVf7HOxvIV+rmYNTeWI64Enqqqf2edjeWQ4T4u5pSPY0uhX8DfJ3mkuwMY4Nuq6rMA3c9v7crHTT2xVqaPGNdPgL3dR+I7T35cZm328zuAY8D7knw8yXuTnM36G8vF+gnrZyyH7Qb+qlteb2N50nAfYUrj2FLo/2BVvQ7YCfxikiteoW6v6SPOUOP6+WfAdwKXA58F/rCruxb7uRF4HfBnVfV9wJcYnAJYzFrsIyzez/U0lgBkcNPn1cBfL1V1TNla7ePUxrGZ0K+qo93PzwMfYvCR6XMnPx52Pz/fVe81fcSZaFw/q+pzVfWVqnoJ+Av+/+PiWuznArBQVQ936/cxCMf1NpZj+7nOxvKkncCjVfW5bn29jSWM9HGa49hE6Cc5O8k3n1wGrgL+hZdPH3E98Lfd8izwtu5qgTcCz538uHkmW6yfI+c9f4pB32ENTpNRVf8JPJPku7uiKxnc8b2uxnKxfq6nsRxyHS8/7bGuxrLzsj5OdRyn/Y326XgwOD/6ie5xCPjNrvw84KPAp7ufr+7Kw+AfxzwFPAFsm3YfVtnPu7t+PN79Ur1maJ/f7Pp5GNg57T707OflwFzXn78BXrXexvIV+rnexvKbgC8C5wyVrauxXKSPUxtH78iVpIY0cXpHkjRg6EtSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1JD/A5+n1hPn+ENZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "\n",
    "def draw_cost(u,W):\n",
    "    #count, bins, ignored =   plt.hist(j(u,W),density=True)\n",
    "    samples=jj(u,W)\n",
    "    max_samples=max(samples)\n",
    "    hist_plot(samples)\n",
    "    return max_samples\n",
    "\n",
    "# poisson , discrete, binomiale\n",
    "pi, wi, W, title = choisir_loi(binomiale)\n",
    "\n",
    "u=49\n",
    "# commence par traiter le problème par simulation (avec W)\n",
    "max_samples=draw_cost(u,W);\n",
    "plt.show()\n",
    "\n",
    "# calcul de la loi exacte\n",
    "valeurs=jj(u,wi) # toutes les valeurs de j(u,wi[i])\n",
    "support = np.sort(list(dict.fromkeys(valeurs))) \n",
    "      # on calcule le support de la loi\n",
    "      # en enlevant les valeurs en double\n",
    "loi=np.zeros(support.size) # on va calculer la loi de j(u,W)\n",
    "for i in range(support.size):\n",
    "    for k in range(wi.size):\n",
    "        if jj(u,wi[k]) == support[i]:\n",
    "            loi[i]=loi[i]+pi[k]\n",
    "\n",
    "# on tronque l'histogramme au delà de la valeur max_samples\n",
    "for imax in range(support.size):\n",
    "    if support[imax] > max_samples:\n",
    "        print(imax);break\n",
    "imax=imax-1\n",
    "            \n",
    "# On trace cet histogramme\n",
    "plt.bar(support[0:imax], loi[0:imax],width=5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Paragraphe 1.6.__  Stratégie $[s,S]$\n",
    "\n",
    "On regarde maintenant un cas ou le vendeur à déjà des journaux et où il paye un coup fixe s'il commande des journaux. \n",
    "On cherche à retrouver ici le fait que la stratégie optimale est de la forme $[s,S]$.\n",
    "\n",
    "__Question 7.__ On se placera dans le cas test=1. Calculer le nombre optimal de journaux à commander \n",
    "suivant la valeur du stock initial. \n",
    "Vérifier que la stratégie est bien de la forme $[s,S]$: \n",
    "on remonte le stock au niveau $S$ si il est inférieur à $s$ et on ne fait rien sinon. \n",
    "\n",
    "On vérifie que $s$ se calcule aussi par la formule\n",
    "$$s := \\sup \\left\\{z ∈ (− ∞, S)|J(z) ≥ cF + J(S )\\right\\} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1) Calcul par une méthode brutale : valeur de s=23.000000 et de S=48.000000\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2) Formule du cours: valeur de s=23.000000 et de S=48.000000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# On regarde maintenant un cas ou le vendeur à déjà des journaux \n",
    "# et ou il paye un coup fixe s'il commande des journaux \n",
    "# on voit une stratégie [s,S] \n",
    "\n",
    "def Jtilde(u,x,pi,wi):\n",
    "    return cf*(u>0) + J(u+x,pi,wi) -c*x\n",
    "\n",
    "# Le but est de verifier que l'on a une stratégie [s,S]\n",
    "\n",
    "# Coix du modèle : poisson , discrete, binomiale\n",
    "pi, wi, W, title = choisir_loi(poisson)\n",
    "\n",
    "# Calcul de S\n",
    "# S=uopt, où uopt est l'argmin de J(u) (cf Slide 11/20)\n",
    "# uopt est caclulé dans la fonction résultat\n",
    "uopt=resultats(pi,wi,dessin='non') # on ne veux pas de dessin ici\n",
    "S=uopt \n",
    "\n",
    "# Il nous faut maintenant calculer s\n",
    "xv=np.linspace(0,2*max(wi), num=200+1);\n",
    "xuopt=xv.copy();\n",
    "U=np.linspace(0,2*max(wi), num=200+1); # \n",
    "Ju=U.copy();\n",
    "\n",
    "for i in range(0, xv.size):\n",
    "    for j in range(0, U.size):\n",
    "        Ju[j]= Jtilde(U[j],xv[i],pi,wi); # à xv[i] stock fixé, on calcule les coûts pour les commandes U[j]  \n",
    "    k = np.argmin(Ju); # on optimize en Ju\n",
    "    xuopt[i]= U[k]; # ca qui nous donne la commande optimale pour le stock initial xv[i]\n",
    "\n",
    "# s = la valeur la plus grande où le contrôle est non nul\n",
    "# on cherche donc l'indice iopt de la valeur la plus petite où le \n",
    "# contrôle est non nul. xv[iopt-1] donne la valeur de s cherchée.\n",
    "iopt=-1;\n",
    "for i in range(0, xuopt.size):\n",
    "    if xuopt[i] == 0:\n",
    "        iopt=i;\n",
    "        break;\n",
    "# (iopt-1) est le dernier indice ou la controle est non nul\n",
    "# et s est la valeur de x correspondante xv[iopt-1]\n",
    "s = xv[iopt-1]\n",
    "print(\"1) Calcul par une méthode brutale : valeur de s=%f et de S=%f\\n\" % (s, S))\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "# on vérifie que pour x en dessous de s, x+uopt=cte=S\n",
    "plt.plot(xv[:int(s)],xv[:int(s)]+xuopt[:int(s)])\n",
    "\n",
    "# au dela xuopt=0 (on ne commande rien), donc on est sur la droite y = x!\n",
    "plt.plot(xv[int(s)+1:150],xv[int(s)+1:150]+xuopt[int(s)+1:150])\n",
    "\n",
    "plt.show()\n",
    "\n",
    "# On vérifie le formule de s donnée dans le cours (p.11 cours-4) fonctionne\n",
    "xv= np.linspace(0,2*max(wi), num=200+1);\n",
    "Jv=np.zeros(xv.size);\n",
    "for i in range(0,xv.size):\n",
    "    Jv[i]=J(xv[i],pi,wi)\n",
    "JS=J(S,pi,wi) # J(S)\n",
    "costs = Jv - (cf + JS);\n",
    "# calcul du plus grand z où J(z) >= c_F + J(S)\n",
    "iopt=-1\n",
    "for i in range(0,xv.size):\n",
    "    if costs[i] <=0:\n",
    "        iopt=i;\n",
    "        break;\n",
    "if iopt < 0: \n",
    "    s=0 \n",
    "else:\n",
    "    s=xv[iopt-1]\n",
    "    \n",
    "print(\"2) Formule du cours: valeur de s=%f et de S=%f\\n\" % (s, S))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Question 6 En utilisant la présentation faite en cours, construire un problème linéaire dont la solution \n",
    "    permet de calculer le nombre de journaux optimal à commander "
   ]
  }
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