Chapter 4, Problem 11T

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12th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781337625340

Textbook Problem

Maximize

To determine

**To calculate:** The solution of the linear programming problem

Maximize

Subject to

Explanation

**Given Information:**

The provided problem is:

Maximize

Subject to

**Formula used:**

Following steps of the simplex method,

Step 1: Use slack variables and write the inequalities in equation form.

Step 2: Write the equations in an augmented matrix.

Step 3: Choose the smallest negative number on the left side of the bottom row and pivot the column.

Step 4: Select the pivot which is the smallest of the test ratios *a* is the entry in the right most column and *b* is the corresponding entry in the pivot column.

Step 5: Clear the pivot column using the pivot and label the pivot row with the label of the pivot column.

Step 6: Repeat the above steps till all the entries in the bottom row are non-negative.

Use row operations to clear the column of the augmented matrix.

**Calculation:**

Consider the maximisation problem,

Maximize

Subject to

Step 1: Use slack variables and write the inequalities in equation form.

Add the slack variables

Step 2: Write the equations in an augmented matrix.

The equations are,

And,

Write the equations in augmented matrix,

Step 3: Choose the smallest negative number on the left side of the bottom row and pivot the column.

Since, the smallest negative number on the left side of the bottom row is

Thus, choose the left most entry and pivot the *x* column.

Step 4: Select the pivot which is the smallest of the test ratios *a* is the entry in the right most column and *b* is the corresponding entry in the pivot column.

Since, the test ratios are neither 0 nor negative.

Thus, the test ratios are

Since,

Thus, the pivot is 4 in column *x*.

Step 5: Clear the pivot column using the pivot and label the pivot row with the label of the pivot column.

Since, the pivot is *x* and replace *x*.

Thus, *x* is the active variable.

Use row operations to clear the pivot column of the augmented matrix.

Use the row operations

Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8E

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