{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Coûts d'une entreprises\n", "\n", "Dans ce TP, on propose d'étudier les coûts d'une entreprises. Nous commencerons pas étudier les coûts \"classiques\" puis le coût moyen et enfin les coûts marginal.\n", "\n", "Des aides sont disponibles à la fin de ce TP." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coût total\n", "\n", "L'étude des coûts totaux d'une entreprise a mené à la formule suivante où $q$ décrit la quantité produite (entre 0 et 500):\n", "$$ Coût(q) = 0.3q^3 + 1.25q^2 + 7,5q + 900$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. En vous inspirant de l'annexe sur les fonctions, programmer la fonction coût." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Calculer les coûts pour 0, 5 et 10 objets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. On souhaite calculer tous les coûts possibles. Pour cela, inspirer vous de l'annexe sur les boucles et les listes pour calculer les coûts pour les quantités allant de 0 à 500." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "quantites = list(range(0, 11))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. En vous inspirant de l'annexe sur les graphiques, tracer le graphique qui permet de visualiser l'évolution de ces coûts." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. Décrire l'évolution des coûts pour cette entreprise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Étude du coût moyen\n", "\n", "Le coût moyen est le coût pour une unité produite. Plus ce coût moyen est faible plus le coût unitaire d'une unité est faible. Ce coût se calcule à partir du coût total avec la formule suivante\n", "$$ C_m(q) = \\frac{C(q)}{q}$$\n", "Dans la suite, on reprend la formule du coût de la partie précédente." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Programmer la fonction qui permet de calculer le coût moyen." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Calculer les coûts moyennes quand les quantités varient de 1 à 500." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Tracer le graphique représentant les coûts moyens" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Décrire la courbe représentative des coûts marginaux. Quelle quantité doit ont produire pour que le coût d'un objet soit le plus faible?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coût marginal\n", "\n", "Le coût marginal est le coût supplémentaire si l'on décide de produire une unité de plus. Il se calcule à partir du coût total avec la formule suivante:\n", "$$ C_M(q) = C(q+1) - C(q)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Programmer la fonction qui permet de calculer le coût marginal.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Calculer le coût marginal pour les quantités allant de 1 à 499." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Tracer le graphique représentant les coûts marginaux." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Décrire la courbe des coûts marginaux. Que peut-on dire du coût de production si l'on chercher à augmenter la production." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Annexe" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Programmer des fonctions\n", "\n", "Les fonctions mathématiques peuvent aisement se programmer avec des fonctions de programmation. Seul la syntaxe change.\n", "\n", "Si l'on souhaite programmer la fonction\n", "\n", "$$ f(x) = \\frac{x + 1}{3x - 1} $$\n", "On écrira" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return (x+1)/(3*x-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quelques éléments sont à noter:\n", "\n", "- Il y a deux points à la fin de la première ligne\n", "- Le mot clé `return` est indenté\n", "- Toutes les opérations sont écrites avec les parenthèses appropriées.\n", "\n", "On pourra ensuite utiliser cette fonction pour calculer des images de nombres. Dans ce cas, la syntaxe est la même qu'en math." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n", "0.3377926421404682\n" ] } ], "source": [ "print(f(1))\n", "print(f(100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Boucles et listes\n", "\n", "En programmation, il existe plusieurs types de variables. Vous connaissez par exemples les `integer` qui sont des nombres entiers, les `string` qui sont les chaines de caractères. Il existe aussi les listes qui permettent de stocker plusieurs valeurs dans une seule variable." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 5, 'a', 10]\n" ] } ], "source": [ "liste = [1, 5, 'a', 10]\n", "print(liste)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut accéder à des valeurs particulières avec des crochets" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1\n", "a\n" ] } ], "source": [ "print(liste[0])\n", "print(liste[2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut ajouter des éléments à une liste" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 5, 'a', 10, 100]\n" ] } ], "source": [ "liste.append(100)\n", "print(liste)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les listes marchent particulièrement bien avec les boucles. On peut alors faire des actions sur chacune des valeurs de la liste." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5\n", "25\n", "aaaaa\n", "50\n", "500\n" ] } ], "source": [ "for valeur in liste:\n", " print(valeur * 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quand on fait des calculs sur des listes, il est utile garder les résultats dans une deuxième liste" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "deuxieme_liste = [] # On crée une liste vide\n", "for valeur in liste:\n", " deuxieme_liste.append(valeur*5)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5, 25, 'aaaaa', 50, 500]\n" ] } ], "source": [ "print(deuxieme_liste)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracer une graphique\n", "\n", "On peut tracer des graphiques à partir de deux listes:\n", "\n", "- la liste des abcisses (les x)\n", "- la liste des ordonnées (les y)\n", "\n", "avant de pouvoir tracer ce graphique, il faut s'assurer d'avoir importer la biliothèque qui permet de les réaliser. Il faut donc valider (une seule fois) les lignes suivantes" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On calcule ou on entre les abscisses et les ordonnées" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "abscisses = [0, 1, 2, 3, 4]\n", "ordonnees = [2, 4, 5, 0, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Et on peut tracer le graphique" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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