Explanation Given Information: The given linear programming problem is: Maximize f = 7 x + 10 y Subject to 14 x + 14 y ≤ 98 8 x + 10 y ≤ 100 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 b , where 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 7 x + 10 y Subject to 14 x + 14 y ≤ 98 8 x + 10 y ≤ 100 x ≥ 0 , y ≥ 0 Step 1: Use slack variables and write the inequalities in equation form. Add the slack variables s and t as below, 14 x + 14 y + s = 98 8 x + 10 y + t = 100 Step 2: Write the equations in an augmented matrix. The equations are, 14 x + 14 y + s = 98 8 x + 10 y + t = 100 And, f − 7 x − 10 y = 0 Write the equations in augmented matrix, [ x y s t f s 14 14 1 0 0 98 t 8 10 0 1 0 100 f − 7 − 10 0 0 1 0 ] 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 − 10 . Thus, choose the second entry in last row and pivot the y column. Step 4: Select the pivot which is the smallest of the test ratios a b , where 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 98 14 = 7 and 100 10 = 10

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 20E

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To calculate: The linear programming problem:

Maximize f=7x+10y

Subject to

14x+14y≤988x+10y≤100

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Chapter 4.3, Problem 19E

Chapter 4.3, Problem 21E

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The linear programming problem: Maximize f = 7 x + 10 y Subject to 14 x + 14 y ≤ 98 8 x + 10 y ≤ 100

Solution Summary: The author explains how to calculate the linear programming problem: Maximize f=7x+10y and write the equations in an augmented matrix.

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To calculate: The linear programming problem:

Maximize f=7x+10y

Subject to

14x+14y≤988x+10y≤100

Want to see the full answer?

Chapter 4 Solutions

The linear programming problem: Maximize f = 7 x + 10 y Subject to 14 x + 14 y ≤ 98 8 x + 10 y ≤ 100

Solution Summary: The author explains how to calculate the linear programming problem: Maximize f=7x+10y and write the equations in an augmented matrix.

Videos

To calculate: The linear programming problem: Maximize f=7x+10y Subject to 14x+14y≤988x+10y≤100

Want to see the full answer?

Chapter 4 Solutions

To calculate: The linear programming problem:

Maximize f=7x+10y

Subject to

14x+14y≤988x+10y≤100