Explanation Given Information: The provided function is f = 12 x + 20 y subject to constraints 3 x + 5 y ≤ 1500 9 x + 5 y ≤ 3600 x + 5 y ≤ 1000 x ≥ 0 , y ≥ 0 Formula used: Steps to find the optimal value of the function using graphical method: Step 1: Write the objective function and inequalities from the problem. Step 2: Graph the solution of the inequalities. Step 3: Find the points of the feasible region. Step 4: Calculate the value of the function at each point of the feasible region. Step 5: Determine the minimum or maximum value of the function according to the question. Calculation: Consider the problem. Maximize f = 12 x + 20 y subject to the constraints { 3 x + 5 y ≤ 1500 9 x + 5 y ≤ 3600 x + 5 y ≤ 1000 x ≥ 0 , y ≥ 0 Consider the inequality 3 x + 5 y ≤ 1500 . First, sketch the graph of 3 x + 5 y = 1500 . Put x = 0 , then y = 30 0 therefore y − intercept is ( 0 , 30 0 ) . Put y = 0 , then x = 500 therefore x − intercept is ( 500 , 0 ) . Now solve 3 x + 5 y ≤ 1500 for y . 3 x + 5 y ≤ 1500 Subtract 3 x from both sides, 3 x + 5 y − 3 x ≤ 1500 − 3 x 5 y ≤ 1500 − 3 x y ≤ − 3 5 x + 300 The graph consists of the half plane below the solid boundary line y = − 3 5 x + 300 . Consider the inequality 9 x + 5 y ≤ 3600 . Now, sketch the graph of 9 x + 5 y = 3600 . Put x = 0 , then y = 7 20 therefore y − intercept is ( 0 , 7 20 ) . Put y = 0 , then x = 400 therefore x − intercept is ( 400 , 0 ) . Now solve 9 x + 5 y ≤ 3600 for y . 9 x + 5 y ≤ 3600 Subtract 9 x from both sides, 9 x + 5 y − 9 x ≤ 3600 − 9 x 5 y ≤ − 9 x + 3600 y ≤ − 9 5 x + 720 The graph also consists of half plane below the solid boundary line y = − 9 5 x + 720 . Consider the inequality x + 5 y ≤ 1000

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 10T

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To calculate: The maximum value of the function f=12x+20y subject to the constraints

3x+5y≤15009x+5y≤3600x+5y≤1000x≥0,y≥0

by using the graphical method.

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Chapter 4, Problem 9T

Chapter 4, Problem 11T

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The maximum value of the function f = 12 x + 20 y subject to the constraints 3 x + 5 y ≤ 1500 9 x + 5 y ≤ 3600 x + 5 y ≤ 1000 x ≥ 0 , y ≥ 0 by using the graphical method.

Solution Summary: The author calculates the maximum value of the function f=12x+20y subject to the constraints.

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To calculate: The maximum value of the function f=12x+20y subject to the constraints

3x+5y≤15009x+5y≤3600x+5y≤1000x≥0,y≥0

by using the graphical method.

Want to see the full answer?

Chapter 4 Solutions

The maximum value of the function f = 12 x + 20 y subject to the constraints 3 x + 5 y ≤ 1500 9 x + 5 y ≤ 3600 x + 5 y ≤ 1000 x ≥ 0 , y ≥ 0 by using the graphical method.

Solution Summary: The author calculates the maximum value of the function f=12x+20y subject to the constraints.

Concept explainers

Videos

To calculate: The maximum value of the function f=12x+20y subject to the constraints 3x+5y≤15009x+5y≤3600x+5y≤1000x≥0,y≥0 by using the graphical method.

Want to see the full answer?

Chapter 4 Solutions

To calculate: The maximum value of the function f=12x+20y subject to the constraints

3x+5y≤15009x+5y≤3600x+5y≤1000x≥0,y≥0

by using the graphical method.