Explanation Given Information: The provided function is f = 70 x + 5 y subject to constraints x + 1.5 y ≤ 150 , x + 0.5 y ≤ 90 , x ≥ 0 , y ≥ 0 . Formula used: The Simplex Method for Problems in Nonstandard Form: 1 . If necessary, convert all inequalities (except x ≥ 0 , y ≥ 0 , ... ) into the form. [Linear expression] ≤ [Constant]. 2 . If a negative number appears in the upper part of the last column of the simplex tableau, remove it by pivoting. (a) Select one of the negative entries in its row. The column containing the entry will be the pivot column. (b) Select the pivot element by determining the least of the positive ratios associated with entries in the pivot column (except the bottom entry). (c) Pivot. 3 . Repeat step 2 until there are no negative entries in the upper part of the right-hand column of the simplex tableau. (If this process will not remove all negative entries from the upper part of the right-hand column, then the linear programming problem does not have an optimal solution.). 4 . Proceed to apply the simplex method for tableaux in standard maximization form. Calculation: Consider the problem. Maximize f = 70 x + 5 y subject to the constraints { x + 1.5 y ≤ 150 x + 0.5 y ≤ 90 x ≥ 0 , y ≥ 0 First, transform the problem from maximization to minimization. Minimize − f = − 70 x − 5 y subject to the constraints { x + 1.5 y ≤ 150 x + 0.5 y ≤ 90 x ≥ 0 , y ≥ 0 Clear the decimal by multiplying each inequality by 2 . Minimize − f = − 70 x − 5 y subject to the constraints { 2 x + 3 y ≤ 300 2 x + y ≤ 180 x ≥ 0 , y ≥ 0 From the above linear system, the simplex tableau is: [ 2 3 1 0 0 300 2 1 0 1 0 180 − 70 − 5 0 0 1 0 ] Since the most negative entry is − 70

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4, Problem 9T

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To calculate: The maximum value of the function f=70x+5y subject to the constraints x+1.5y≤150,x+0.5y≤90,x≥0,y≥0 by using the simplex method.

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Chapter 4, Problem 8T

Chapter 4, Problem 10T

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The maximum value of the function f = 70 x + 5 y subject to the constraints x + 1.5 y ≤ 150 , x + 0.5 y ≤ 90 , x ≥ 0 , y ≥ 0 by using the simplex method.

Solution Summary: The author calculates the maximum value of the function f=70x+5y subject to the constraints by using the simplex method.

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To calculate: The maximum value of the function f=70x+5y subject to the constraints x+1.5y≤150,x+0.5y≤90,x≥0,y≥0 by using the simplex method.

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