Explanation Given Information: The linear programing problem with mixed constraint is given as: Maximize f = 2 x + 5 y subject to − x + y ≤ 10 x + y ≤ 30 − 2 x + y ≥ − 24 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: Provided the LPP is, Maximize f = 2 x + 5 y subject to the constraints − x + y ≤ 10 x + y ≤ 30 − 2 x + y ≥ − 24 Since, above maximization problem has mixed constraint so first convert all the constraints into standard form. Convert all constraints as ≥ into ≤ by multiplying them by ( − 1 ) both side. Here − 2 x + y ≥ − 24 is in ≥ , convert it into ≤ . 2 x − y ≤ 24 Express all constraints as ≤ constraints. To form the simplex form convert all the inequalities into equations, add slack variable into the inequalities. − x + y + s 1 = 10 x + y + s 2 = 30 − 2 x + y + s 3 = − 24 x ≥ 0 , y ≥ 0 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 s 1 s 2 s 3 f [ − 1 1 1 0 0 0 10 1 1 0 1 0 0 30 2 − 1 0 0 1 0 24 − 2 − 5 0 0 0 1 0 ] Since, -5 is the most negative entry therefore 2 nd column is pivot column and ratio is minimum in first row corresponding to element 1, hence 1 is pivot element for this table. Solve the given problem by simplex method

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4.5, Problem 17E

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

Maximize f=2x+5y subject to

−x+y≤10x+y≤30−2x+y≥−24

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Chapter 4.5, Problem 16E

Chapter 4.5, Problem 18E

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The optimal solution of the LPP with the help of simplex method. Maximize f = 2 x + 5 y subject to − x + y ≤ 10 x + y ≤ 30 − 2 x + y ≥ − 24

Solution Summary: The author explains how to calculate the optimal solution of the linear programming problem by simplex method.

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

Maximize f=2x+5y subject to

−x+y≤10x+y≤30−2x+y≥−24

Want to see the full answer?

Chapter 4 Solutions

The optimal solution of the LPP with the help of simplex method. Maximize f = 2 x + 5 y subject to − x + y ≤ 10 x + y ≤ 30 − 2 x + y ≥ − 24

Solution Summary: The author explains how to calculate the optimal solution of the linear programming problem by simplex method.

Videos

To calculate: The optimal solution of the LPP with the help of simplex method. Maximize f=2x+5y subject to −x+y≤10x+y≤30−2x+y≥−24

Want to see the full answer?

Chapter 4 Solutions

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

Maximize f=2x+5y subject to

−x+y≤10x+y≤30−2x+y≥−24