Explanation Given Information: The provided optimization problem is given as Maximize f = 5 x + 30 y subject to 2 x + 10 y ≤ 96 x + 10 y ≤ 90 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. Calculation: Consider the provided function, Maximize f = 5 x + 30 y subject to 2 x + 10 y ≤ 96 x + 10 y ≤ 90 To form the simplex table convert all the inequalities into equations by adding slack variable into the inequalities. 2 x + 10 y + s 1 = 96 x + 10 y + s 2 = 90 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 [ 2 10 1 0 0 96 1 10 0 1 0 90 − 5 − 30 0 0 1 0 ] Now, to find the pivot element, first find the pivot row and pivot column. Most negative value in last row is ( − 30 ) in second column therefore variable y will enter in the simplex table. To finding the leaving variable, calculate minimum ratio. Minimum ratio = min { 96 10 , 90 10 } = 9 Second row is pivot row and leave the table. Pivot element is 10. Apply the row operations to solve this matrix: R 1 → R 1 − 1 10 R 2 → R 2 The simplex matrix will become: x y s 1 s 2 f [ 2 10 1 0 0 96 1 10 1 0 1 10 0 9 − 5 − 30 0 0 1 0 ] As − 30 is the most negative entry, the second column is the pivot column

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4.3, Problem 22E

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To calculate: The optimal solution of the maximization problem with the help of simplex method.

Maximize f=5x+30y subject to

2x+10y≤96x+10y≤90

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Chapter 4.3, Problem 21E

Chapter 4.3, Problem 23E

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The optimal solution of the maximization problem with the help of simplex method. Maximize f = 5 x + 30 y subject to 2 x + 10 y ≤ 96 x + 10 y ≤ 90

Solution Summary: The author calculates the optimal solution of the linear programming problem with the help of simplex method.

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To calculate: The optimal solution of the maximization problem with the help of simplex method.

Maximize f=5x+30y subject to

2x+10y≤96x+10y≤90

Want to see the full answer?

Chapter 4 Solutions

The optimal solution of the maximization problem with the help of simplex method. Maximize f = 5 x + 30 y subject to 2 x + 10 y ≤ 96 x + 10 y ≤ 90

Solution Summary: The author calculates the optimal solution of the linear programming problem with the help of simplex method.

Videos

To calculate: The optimal solution of the maximization problem with the help of simplex method. Maximize f=5x+30y subject to 2x+10y≤96x+10y≤90

Want to see the full answer?

Chapter 4 Solutions

To calculate: The optimal solution of the maximization problem with the help of simplex method.

Maximize f=5x+30y subject to

2x+10y≤96x+10y≤90