Explanation Given Information: The given function is, f = 3 x + 2 y And the given inequalities are, x + 2 y ≤ 48 x + y ≤ 30 2 x + y ≤ 50 x + 10 ≤ 200 Formula used: The mixed constraints by the use of Simplex method, (1) The problem is to maximize use f and to minimize use − f . (2) Make all the constraints to ≤ by multiply − 1 both the sides of the constraint and use slack variable to make simplex matrix. (3) Check the negative entry in the upper portion of the last column if entries are negative go to step 4 otherwise apply simplex method. (4) select the negative entry in the same row and take that column as pivot column. In pivot column find all quotients above the line for the entries then find the pivot from the smallest positive quotient. Then after completing the operation go to step 3. Calculation: Consider the given function and inequalities, f = 3 x + 2 y Subject to: x + 2 y ≤ 48 x + y ≤ 30 2 x + y ≤ 50 x + 10 ≤ 200 Introducing the slack variables and rewriting the objective function, x + 2 y + s 1 = 48 x + y + s 2 = 30 2 x + y + s 3 = 50 x + 10 y + s 4 = 200 − 3 x − 2 y + f = 0 Write this in a matrix with the objective function in the last row, x y s 1 s 2 s 3 s 4 f [ 1 2 1 0 0 0 0 48 1 1 0 1 0 0 0 30 ( 2 ) 1 0 0 1 0 0 50 1 10 0 0 0 1 0 200 − 3 − 2 0 0 0 0 1 0 ] Most negative value in the last row is − 3 . So, x is the pivot column. Now divide the constants of pivot column from the last row as, 48 / 1 = 48 30 / 1 = 30 50 / 2 = 25 200 / 1 = 200 Here 25 is the smallest quotient. So, 2 is the pivot entry. The pivot entry is shown in the matrix inside brackets. Now, multiply the Row 3 with 1 / 2 to get pivot entry as 1, [ 1 2 1 0 0 0 0 48 1 1 0 1 0 0 0 30 ( 1 ) 1 2 0 0 1 2 0 0 25 1 10 0 0 0 1 0 200 − 3 − 2 0 0 0 0 1 0 ] Now use operations with other rows to make all other entries in the pivot column equal to zero. So, use the following operations, Add − 1 times row 3 to row 1, Add − 1 times row 3 to row 2, Add − 1 times row 3 to row 4, Add 3 times row 3 to row 5

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, Problem 19RE

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To calculate: The following linear programming problem using simplex method assuming that all the variables are non-negative.

Maximize f=3x+2y subject to:

x+2y≤48x+y≤302x+y≤50x+10≤200

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Chapter 4 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

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The following linear programming problem using simplex method assuming that all the variables are non-negative. Maximize f = 3 x + 2 y subject to: x + 2 y ≤ 48 x + y ≤ 30 2 x + y ≤ 50 x + 10 ≤ 200

Solution Summary: The author calculates the linear programming problem using simplex method assuming that all variables are non-negative.

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To calculate: The following linear programming problem using simplex method assuming that all the variables are non-negative.

Maximize f=3x+2y subject to:

x+2y≤48x+y≤302x+y≤50x+10≤200

Chapter 4 Solutions

The following linear programming problem using simplex method assuming that all the variables are non-negative. Maximize f = 3 x + 2 y subject to: x + 2 y ≤ 48 x + y ≤ 30 2 x + y ≤ 50 x + 10 ≤ 200

Solution Summary: The author calculates the linear programming problem using simplex method assuming that all variables are non-negative.

Videos

To calculate: The following linear programming problem using simplex method assuming that all the variables are non-negative. Maximize f=3x+2y subject to: x+2y≤48x+y≤302x+y≤50x+10≤200

Chapter 4 Solutions

To calculate: The following linear programming problem using simplex method assuming that all the variables are non-negative.

Maximize f=3x+2y subject to:

x+2y≤48x+y≤302x+y≤50x+10≤200