Explanation Given: The objective function is z = 3 x + 5 y . Linear equalities representing constraints are as follows: x + y ≤ 6 x ≥ 2 x ≥ 0 y ≥ 0 . Calculation: Consider the inequalities and substitute the equal symbol at the place of inequality and rewrite the equation as shown below: Find two solutions of the linear equation to plot the graph of the linear equation x + y = 6 To find the value of x -intercept, substitute y = 0 as shown below: x + y = 6 x + 0 = 6 x = 6 To find the value of y -intercept, substitute x = 0 as shown below: 0 + y = 6 y = 6 Thus, plot the intercepts ( 6 , 0 ) and ( 0 , 6 ) and draw a solid line passing through these points because inequality contains ≤ symbol in which equality is included. Now, this solid line divides the plane into three regions: the line itself and two half planes. Now, take origin ( 0 , 0 ) as a test point and check the region in the graph to shade: Check whether the test point satisfies the inequality: x + y ≤ 6 0 + 0 ≤ ? 6 0 ≤ 6 Since the test point satisfies the inequality, shade the half plane containing thetest point, that is, origin ( 0 , 0 ) . To plot the graph of the inequality x ≥ 0 , graph the line x = 0 which is a vertical line parallel to y- axis and shade the right part as the inequality contains ≥ symbol. Similarly, to plot the graph of the inequality y ≥ 0 , graph the line y = 0 which is a horizontal line parallel to x- axis and shade the upper part as the inequality contains ≥ symbol. Similarly, to plot the graph of x ≥ 2 , graph the line x = 2 and shade the right part as the inequality contains ≥ symbol

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ISBN: 9780100577541

Author: Blitzer

Publisher: YUZU

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Chapter 8, Problem 11T

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To calculate: The maximum value of z=3x+5y subject to the constraints x+y≤6x≥2x≥0y≥0.

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Chapter 8, Problem 10T

Chapter 8, Problem 12T

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The maximum value of z = 3 x + 5 y subject to the constraints x + y ≤ 6 x ≥ 2 x ≥ 0 y ≥ 0 .

Solution Summary: The author calculates the maximum value of z=3x+5y subject to the constraints. Linear equalities representing constraints are as follows:

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To calculate: The maximum value of z=3x+5y subject to the constraints x+y≤6x≥2x≥0y≥0.

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Chapter 8 Solutions