Explanation Given Information: The provided matrix is: Minimize c = 4 x + y + z + w Subject to x + y ≥ 30 , y − z ≤ 20 , z − w ≤ 10 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0 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 provided matrix is: Minimize c = 4 x + y + z + w Subject to x + y ≥ 30 , y − z ≤ 20 , z − w ≤ 10 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0 Step 1) Use slack variables and write the inequalities in equation form. x + y − s = 30 y − z + t = 20 z − w + u = 10 And, 4 x + y + z + w + p = 0 Step 2) Write the equations in an augmented matrix. x y z w s t u p s 1 1 0 0 − 1 0 0 0 30 t 0 1 − 1 0 0 1 0 0 20 u 0 0 1 − 1 0 0 1 0 10 p 4 1 1 1 0 0 0 1 0 Step 3) Choose the smallest negative number on the left side of the bottom row and pivot the column. The most negative entry in the bottom row is the 1 in the x − column Thus, pivot on the 1 in the u − row. x y z w s t u p s 1 1 0 0 − 1 0 0 0 30 t 0 1 − 1 0 0 1 0 0 20 u 0 0 1 − 1 0 0 1 0 10 p 4 1 1 1 0 0 0 1 0 Apply row operation R 4 − 4 R 1 ; x y z w s t u p x 1 1 0 0 − 1 0 0 0 30 t 0 1 − 1 0 0 1 0 0 20 u 0 0 1 − 1 0 0 1 0 10 p 0 − 3 1 1 4 0 0 1 − 120 There are no more starred rows

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 6, Problem 18RE

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To calculate: The linear programming problem using simplex method.

Minimize c=4x+y+z+w

Subject to x+y≥30,y−z≤20,z−w≤10 and x≥0,y≥0,z≥0,w≥0

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Chapter 6, Problem 17RE

Chapter 6, Problem 19RE

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Chapter 6 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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The linear programming problem using simplex method. Minimize c = 4 x + y + z + w Subject to x + y ≥ 30 , y − z ≤ 20 , z − w ≤ 10 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0

Solution Summary: The author calculates the linear programming problem using simplex method. They use slack variables and write inequalities in equation form.

Videos

To calculate: The linear programming problem using simplex method.

Minimize c=4x+y+z+w

Subject to x+y≥30,y−z≤20,z−w≤10 and x≥0,y≥0,z≥0,w≥0

Want to see the full answer?

Chapter 6 Solutions

The linear programming problem using simplex method. Minimize c = 4 x + y + z + w Subject to x + y ≥ 30 , y − z ≤ 20 , z − w ≤ 10 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0

Solution Summary: The author calculates the linear programming problem using simplex method. They use slack variables and write inequalities in equation form.

Videos

To calculate: The linear programming problem using simplex method. Minimize c=4x+y+z+w Subject to x+y≥30,y−z≤20,z−w≤10 and x≥0,y≥0,z≥0,w≥0

Want to see the full answer?

Chapter 6 Solutions

To calculate: The linear programming problem using simplex method.

Minimize c=4x+y+z+w

Subject to x+y≥30,y−z≤20,z−w≤10 and x≥0,y≥0,z≥0,w≥0