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Solve the linear programming problem using the simplex method. 5x + y ≤ 80 9x + 2y ≤ 100 x≥0,y 20 Maximize 2x + 9y subject to the constraints Find the solution. x=y=₁M = (Type integers or decimals.)

Solve the linear programming problem using the simplex method. 5x + y ≤ 80 9x + 2y ≤ 100 x≥0,y 20 Maximize 2x + 9y subject to the constraints Find the solution. x=y=₁M = (Type integers or decimals.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Title: Solving Linear Programming Problems Using the Simplex Method** **Objective:** Solve the linear programming problem using the simplex method. **Problem Statement:** Maximize the function: \[ 2x + 9y \] **Subject to the Constraints:** 1. \( 5x + y \leq 80 \) 2. \( 9x + 2y \leq 100 \) 3. \( x \geq 0, \, y \geq 0 \) **Solution:** Determine the values of \( x \), \( y \), and the maximum value \( M \) such that: - \( x = \_\_\_ \) - \( y = \_\_\_ \) - \( M = \_\_\_ \) **Instructions:** (Type integers or decimals in the blank spaces.) In this exercise, you will learn how to apply the simplex algorithm to find the optimal solution for a set of linear inequalities and objective function.
Transcribed Image Text:**Title: Solving Linear Programming Problems Using the Simplex Method** **Objective:** Solve the linear programming problem using the simplex method. **Problem Statement:** Maximize the function: \[ 2x + 9y \] **Subject to the Constraints:** 1. \( 5x + y \leq 80 \) 2. \( 9x + 2y \leq 100 \) 3. \( x \geq 0, \, y \geq 0 \) **Solution:** Determine the values of \( x \), \( y \), and the maximum value \( M \) such that: - \( x = \_\_\_ \) - \( y = \_\_\_ \) - \( M = \_\_\_ \) **Instructions:** (Type integers or decimals in the blank spaces.) In this exercise, you will learn how to apply the simplex algorithm to find the optimal solution for a set of linear inequalities and objective function.
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