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January 6, 2026 19:42
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profit_modeling_eng.ipynb
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "id": "dcec6df6", | |
| "metadata": {}, | |
| "source": [ | |
| "### Dependencies" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 26, | |
| "id": "c3c85e6e", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import sympy as sp # pyright: ignore[reportMissingImports]\n", | |
| "symbol_x = sp.symbols('x')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "7712e22c", | |
| "metadata": {}, | |
| "source": [ | |
| "### profit function to consider" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 27, | |
| "id": "b4acb4d9", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "-2*x**2 + 120*x - 1000\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "def f(x):\n", | |
| " # return (x**2 - 1) / (x - 1)\n", | |
| " # return (-2*(x**2) + 120 * x - 1000) / x\n", | |
| "\n", | |
| " return -2*(x**2) + 120 * x - 1000\n", | |
| " # return -(x**2) - 10 * x - 16\n", | |
| "\n", | |
| "sympy_f = f(sp.symbols('x'))\n", | |
| "print(sympy_f)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "328be42b", | |
| "metadata": {}, | |
| "source": [ | |
| "### root of profit function" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 28, | |
| "id": "6014e3b4", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "function for total profit: -2*x**2 + 120*x - 1000\n", | |
| "when x = [10, 50] the total profit is 0\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "roots = sp.solve(sympy_f, sp.symbols('x'))\n", | |
| "print(\"function for total profit:\", sympy_f)\n", | |
| "\n", | |
| "print(\"when x =\", roots, \"the total profit is 0\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 29, | |
| "id": "1548b900", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "import numpy as np # pyright: ignore[reportMissingImports]\n", | |
| "import matplotlib.pyplot as plt # pyright: ignore[reportMissingImports]\n", | |
| "\n", | |
| "def plot_profit_func():\n", | |
| " # Generate x values avoiding the undefined point\n", | |
| " x_values = np.linspace(0, 100, 100)\n", | |
| " y_values = f(x_values)\n", | |
| "\n", | |
| " plt.plot(x_values, y_values, label=r\"$f(x)$\")\n", | |
| " # plt.axvline(1, color='r', linestyle='--', label=r\"$x=1$ (undefined)\")\n", | |
| " # plt.axhline(2, color='g', linestyle='--', label=r\"$\\lim_{x \\rightarrow 1} f(x) = L$\")\n", | |
| " plt.title(f\"t-profit for x products sold f(x) = {sympy_f}\")\n", | |
| " plt.xlabel(r\"$x$\")\n", | |
| " plt.ylabel(r\"$f(x)$\")\n", | |
| " plt.legend()\n", | |
| " plt.grid(True)\n", | |
| " plt.xticks(np.arange(0, 101, 10))\n", | |
| " plt.scatter(roots, [0 for _ in roots], color='g')\n", | |
| " plt.show()\n", | |
| "plot_profit_func()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 30, | |
| "id": "d26a6bb8", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "starting profit (0 products sold) is: -1000\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print(\"starting profit (0 products sold) is:\", f(0))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 31, | |
| "id": "c4a37f8d", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "func for marginal profit: 120 - 4*x\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "derivative_f_expr = sp.diff(sympy_f, sp.symbols('x'))\n", | |
| "derivative_f = sp.lambdify(sp.symbols('x'), sp.diff(sympy_f, sp.symbols('x')), 'numpy')\n", | |
| "\n", | |
| "\n", | |
| "print(\"func for marginal profit:\", derivative_f_expr)\n", | |
| "x_values = np.linspace(0, 100, 100)\n", | |
| "y_values = derivative_f(x_values)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 32, | |
| "id": "47aa3cad", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "def plot_marginal_profit_func():\n", | |
| " # Generate x values avoiding the undefined point\n", | |
| " x_values = np.linspace(0, 100, 100)\n", | |
| " y_values = derivative_f(x_values)\n", | |
| " # y_values = f(x_values)\n", | |
| "\n", | |
| " plt.plot(x_values, y_values, label=r\"$f'(x)$\")\n", | |
| " # plt.axvline(1, color='r', linestyle='--', label=r\"$x=1$ (undefined)\")\n", | |
| " # plt.axhline(2, color='g', linestyle='--', label=r\"$\\lim_{x \\rightarrow 1} f(x) = L$\")\n", | |
| " plt.title(f\"marginal profit f(x) = {0}\")\n", | |
| " plt.xlabel(r\"$x$\")\n", | |
| " plt.ylabel(r\"$f(x)$\")\n", | |
| " plt.legend()\n", | |
| " plt.grid(True)\n", | |
| " plt.xticks(np.arange(0, 101, 10))\n", | |
| " roots = sp.solve(derivative_f_expr, sp.symbols('x'))\n", | |
| " plt.scatter(roots, [0 for _ in roots], color='g')\n", | |
| " plt.show()\n", | |
| "plot_marginal_profit_func()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 33, | |
| "id": "87b52622", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "by solving f'(x), we may discover critical point candidates: [30, 0]\n", | |
| "when producing exactly 30 products, there being a max profit of 800\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "critical_points = [p for p in sp.solve(derivative_f_expr, symbol_x) if p > 0] + [0]\n", | |
| "\n", | |
| "results = {p: f(p) for p in critical_points}\n", | |
| "\n", | |
| "max_value = max(results.values())\n", | |
| "\n", | |
| "best_p = max(results, key=results.get)\n", | |
| "\n", | |
| "print(f\"by solving f'(x), we may discover critical point candidates: {critical_points}\")\n", | |
| "\n", | |
| "print(f\"when producing exactly {best_p} products, there being a max profit of {max_value}\")" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "base", | |
| "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": "3.13.7" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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