Consider the following linear programing problem:Maximize Z = 2X1 + 4X2 + 3X3Subject to: 3X₁ +4X2+2X3 ≤ 602X₁ + X2 + 2X3≤ 40X₁ + 3X2 + 2X3X₁, X2, X3 ≥ 0≤80Solve the problem using the Simplex Method in tabular form. (All tableaus andcalculations must be shown).

Given information:Objective function to maximize: Constraints:Non-negativity constraints: To…

Answered: Consider the following linear…

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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Question

Consider the following linear programing problem:
Maximize Z = 2X1 + 4X2 + 3X3
Subject to: 3X₁ +4X2+2X3 ≤ 60
2X₁ + X2 + 2X3
≤ 40
X₁ + 3X2 + 2X3
X₁, X2, X3 ≥ 0
≤80
Solve the problem using the Simplex Method in tabular form. (All tableaus and
calculations must be shown).

Expert Solution

Step 1: Introduction

Given information:

Objective function to maximize: $Z space equals space 2 x subscript 1 space plus space 4 x subscript 2 space plus space 3 x subscript 3$
Constraints:
1. $3 x subscript 1 space plus space 4 x subscript 2 space plus space 2 x subscript 3 space less or equal than space 60$
2. $2 x subscript 1 space plus space x subscript 2 space plus space 2 x subscript 3 space less or equal than space 40$
3. $x subscript 1 space plus space 3 x subscript 2 space plus space 2 x subscript 3 space less or equal than space 80$
Non-negativity constraints: $x subscript 1 comma space x subscript 2 comma space x subscript 3 space greater or equal than space 0$

To find:

Solve the linear programming problem using the Simplex Method to maximize the objective function $Z$ , subject to the given constraints.

Concept used:

The Simplex Method is an iterative technique used to solve linear programming problems. It starts with an initial feasible solution and iteratively moves towards an optimal solution while ensuring that the constraints are satisfied at each step. The method involves constructing a simplex tableau, selecting an entering variable and a departing variable, and performing row operations to pivot to a new solution.