EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Chapter 7.6, Problem 36E
To determine
Todo:Sketcha graph of the solution region corresponding to the system of constraints given below. Then find the minimum and maximum values of the objective function and the points where they occur, subject to the constraints.
Objective function:
Constraints:
Expert Solution & Answer
Answer to Problem 36E
The region corresponding to the system of constraints is
The minimum value of
The maximum value of
Explanation of Solution
Given:
Objective function:
Constraints:
Concept Used:
To find the minimum and maximum values of the objective function.
First plot the given constraints on the graph and find the bounded region. Then evaluating the objective function at each of the vertex of the bounded region results into the minimum and maximum value of the function.
Calculation:
For the given
Objective function:
Constraints:
Plotting the given constraints on a graph,
Let
Consider the equation
Consider
At
At
Plotting the region bounded by the given constraints, we have
The graph of the solution region is abounded region in the shape of trapezium.
Evaluating the objective function at each vertex
At
At
At
At
The minimum value of
The maximum value of
Conclusion:
The region corresponding to the system of constraints is
The minimum value of
The maximum value of
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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