Plotting Department Constraints for Production Optimization

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Production Constraints Graph for Department 1 and Department 2

Prompt

Illustrate a two-dimensional graph where the x-axis represents tables and the y-axis represents chairs. Draw two lines for Department 1 and Department 2 using the equations 3x + 6y = 120 and 6x + 3y = 96, respectively. The intercepts for Department 1 line are at (0, 20) and (40, 0) and for Department 2 line are at (0, 32) and (16, 0). Shade the area below each line to show the production limitations due to department hours. Highlight the overlapping shaded region, which represents the feasible zone where both constraints are met simultaneously.

Original Prompt: C. Preparing the Graph: Convert inequalities to equations for plotting: Department 1: 3x + 6y = 120 Department 2: 6x + 3y = 96 Plot the department constraints: Mark the x-axis (tables) and y-axis (chairs) clearly. Plot each equation as a line, remembering to pay attention to intercepts. Department 1 line: intercepts are (0, 20) and (40, 0). Department 2 line: intercepts are (0, 32) and (16, 0). Identify the feasible region: Shade the area below each line, representing limitations on production due to department hours. The feasible region is the overlapping shaded area where both constraints are satisfied simultaneously.

Model: Imagen 4

Created on 2/1/2024 Report

Updated on 8/9/2025

License: Free to use with a backlink to Easy-Peasy.AI

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