Explanation Given Information: The provided optimization problem is given as Maximize f = 8 x + 6 y subject to 4 x + 3 y ≤ 24 10 x + 9 y ≤ 198 Formula used: To solve the linear programming problem by simplex method, follow the steps below: Step 1: Use slack variables and write the constraint inequalities in equation form. Step 2: Write the equations in a simplex matrix. Step 3: Choose the most negative number on the left side of the bottom row and pivot the column. Step 4: Select the pivot entry which is the smallest of the test ratios a b , where, a is entry in the right most column and b is the corresponding entry in the pivot column. Step 5: Make the pivot entry as 1 and other entries of pivot column as 0 by the use of row operations. Step 6: Repeat the above steps till all the entries in the bottom row are non-negative. If a simplex table at any stage has negative entry in last row but corresponding quotients are not positive, then the problem does not have any solution. If the final simplex table has zero indicator corresponding to non-basic variable then that column will become pivot column and the problem has multiple solution exist. Calculation: Consider the provided function, Maximize f = 8 x + 6 y subject to 4 x + 3 y ≤ 24 10 x + 9 y ≤ 198 To form the simplex table convert all the inequalities into equations by adding slack variable into the inequalities. 4 x + 3 y + s 1 = 24 10 x + 9 y + s 2 = 198 x ≥ 0 , y ≥ 0 Where s 1 and s 2 are two slack variables with s 1 , s 2 ≥ 0 . Simplex matrix for the LPP is written below: x y s 1 s 2 f [ 4 3 1 0 0 24 10 9 0 1 0 198 − 8 − 6 0 0 1 0 ] Most negative element in last row is ( − 8 ) , x -column is pivot column and will enter into matrix and row 1 has least quotient; pivot element is 4

Mathematical Applications for the Management, Life, and Social Sciences

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ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4.3, Problem 38E

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To calculate: The optimal solution of the maximization problem with the help of simplex method also indicate if there is no solution or multiple solution exists.

Maximize f=8x+6y subject to

4x+3y≤2410x+9y≤198

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Chapter 4.3, Problem 37E

Chapter 4.3, Problem 39E

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The optimal solution of the maximization problem with the help of simplex method also indicate if there is no solution or multiple solution exists. Maximize f = 8 x + 6 y subject to 4 x + 3 y ≤ 24 10 x + 9 y ≤ 198

Solution Summary: The author explains how to solve the linear programming problem by simplex method.

Videos

To calculate: The optimal solution of the maximization problem with the help of simplex method also indicate if there is no solution or multiple solution exists.

Maximize f=8x+6y subject to

4x+3y≤2410x+9y≤198

Want to see the full answer?

Chapter 4 Solutions

The optimal solution of the maximization problem with the help of simplex method also indicate if there is no solution or multiple solution exists. Maximize f = 8 x + 6 y subject to 4 x + 3 y ≤ 24 10 x + 9 y ≤ 198

Solution Summary: The author explains how to solve the linear programming problem by simplex method.

Videos

To calculate: The optimal solution of the maximization problem with the help of simplex method also indicate if there is no solution or multiple solution exists. Maximize f=8x+6y subject to 4x+3y≤2410x+9y≤198

Want to see the full answer?

Chapter 4 Solutions

To calculate: The optimal solution of the maximization problem with the help of simplex method also indicate if there is no solution or multiple solution exists.

Maximize f=8x+6y subject to

4x+3y≤2410x+9y≤198