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12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

Chapter 4.5, Problem 13E

Textbook Problem

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In Problems 11-18, use the simplex method to find the optimal solution. Assume that all variables are nonnegative.

Minimize

To determine

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

Minimize

**Given Information:**

The linear programing problem with mixed constraint is given as:

Minimize

**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 *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, Minimize

Minimize

Since, given problem is minimization problem with mixed constraint so first convert it into maximization and also convert all constraint into standard form as

Maximize

Express all constraints as

Where

Simplex matrix for the LPP is written below:

Here,

Solve the given problem by simplex method

Mathematical Applications for the Management, Life, and Social Sciences

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