(a) Explanation Given: The given objective function is z = 2 x + 3 y The constraints are as follows: { x ≥ 0 , y ≥ 0 2 x + y ≤ 8 2 x + 3 y ≤ 12 Graph: Consider the following linear inequalities which represents constraints { x ≥ 0 , y ≥ 0 2 x + y ≤ 8 2 x + 3 y ≤ 12 Now, consider the first linear inequality. 2 x + y ≤ 8 The equation will pass through the following coordinates. x y 0 8 4 0 Now, consider a test point ( 0 , 0 ) to c (b) To determine To calculate: The value of the objective function z = 2 x + 3 y at each corner of graphed region. (c) To determine To calculate: The maximum value of the objective function z = 2 x + 3 y and also determine the values of x and y for which maximum occurs.

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ISBN: 9780136922179

Author: Blitzer

Publisher: RENT PEARS

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Chapter 8.6, Problem 6E

(a)

To determine

To graph: The system of linear inequalities representing constraints {x≥0,y≥02x+y≤82x+3y≤12

(b)

To determine

To calculate: The value of the objective function z=2x+3y at each corner of graphed region.

(c)

To determine

To calculate: The maximum value of the objective function z=2x+3y and also determine the values of x and y for which maximum occurs.

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Chapter 8.6, Problem 5E

Chapter 8.6, Problem 7E

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Chapter 8 Solutions

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To graph: The system of linear inequalities representing constraints { x ≥ 0 , y ≥ 0 2 x + y ≤ 8 2 x + 3 y ≤ 12

Solution Summary: The author explains the system of linear inequalities representing constraints. The graph will be shaded towards the origin.

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To graph: The system of linear inequalities representing constraints {x≥0,y≥02x+y≤82x+3y≤12

To calculate: The value of the objective function z=2x+3y at each corner of graphed region.

To calculate: The maximum value of the objective function z=2x+3y and also determine the values of x and y for which maximum occurs.

Want to see the full answer?

Chapter 8 Solutions