ToFind:The minimum and maximum values of the objective function and the points where they occur, subject to the constraints.
Objective function:
Constraints:

Answer to Problem 25E
The minimum value of
There is no 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
and
and
Consider
At
At
Consider
At
At
Consider
At
At
Plotting the region bounded by the given constraints, we have
Evaluating the objective function at each vertex
At
At
At
The minimum value of
Since, the objective function has positive values only and in the bounded region first quadrant all values are positive so there will be no maximum value.
There is no maximum value of
Conclusion:
The minimum value of
There is no maximum value of
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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