Explanation Given Information: The provided optimization problem is given as Maximize f = 7 x + 10 y + 4 z subject to 3 x + 5 y + 4 z ≤ 30 3 x + 2 y ≤ 4 x + 2 y ≤ 8 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 = 7 x + 10 y + 4 z subject to 3 x + 5 y + 4 z ≤ 30 3 x + 2 y ≤ 4 x + 2 y ≤ 8 To form the simplex table convert all the inequalities into equations by adding slack variable into the inequalities. 3 x + 5 y + 4 z + s 1 = 30 3 x + 2 y + s 2 = 4 x + 2 y + s 3 = 8 Where s 1 , s 2 and s 3 are two slack variables with s 1 , s 2 , s 3 ≥ 0 . Simplex matrix for the LPP is written below: x y z s 1 s 2 s 3 f [ 3 5 4 1 0 0 0 30 3 2 0 0 1 0 0 4 1 2 0 0 0 1 0 8 − 7 − 10 − 4 0 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 ( − 10 ) in second column therefore variable y will enter in the simplex table. To finding the leaving variable, calculate minimum ratio. Minimum ratio = min { 30 5 , 4 2 , 8 2 } = 2 Second row is pivot row and leave the table. Pivot element is 2

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 25E

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

Maximize f=7x+10y+4z subject to

3x+5y+4z≤303x+2y≤4x+2y≤8

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Chapter 4.3, Problem 24E

Chapter 4.3, Problem 26E

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The optimal solution of the maximization problem with the help of simplex method. Maximize f = 7 x + 10 y + 4 z subject to 3 x + 5 y + 4 z ≤ 30 3 x + 2 y ≤ 4 x + 2 y ≤ 8

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=7x+10y+4z subject to

3x+5y+4z≤303x+2y≤4x+2y≤8

Want to see the full answer?

Chapter 4 Solutions

The optimal solution of the maximization problem with the help of simplex method. Maximize f = 7 x + 10 y + 4 z subject to 3 x + 5 y + 4 z ≤ 30 3 x + 2 y ≤ 4 x + 2 y ≤ 8

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=7x+10y+4z subject to 3x+5y+4z≤303x+2y≤4x+2y≤8

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=7x+10y+4z subject to

3x+5y+4z≤303x+2y≤4x+2y≤8