To calculate: the optimal profit.
Answer to Problem 64E
For crop A optimal number of acres is 60
For crop B optimal number of acres is 90
Optimal profit is $33150
Explanation of Solution
Given information:
Two crops A and B are grown. Sum of land of crop A and crop B is at most 150 acres. Total time for trimming crop A and 2 times of crop B is at most 240 hours. Time for picking 30% of crop A and 10% of crop B is at most 30 hours. The profit is $185 per acre for crop A and $245 per acre for crop B.
Calculation:
Let x be the number of acres for crop A and y be the number of acres for crop B.
Total land is at most 150 acres, so
Total time for trimming crop A and 2 times for crop B is at most 240 hours, so
Total time for picking 30% of crop A and 10% of crop B is at most 30 hours, so
From above equations we can plot the graph
For
Plot the points and join them.
The region for
For
Plot the points and join them.
The region for
For
Plot the points and join them.
The region for
Profit function (Objective function)
Now from graph we have set of 5 points:
Now put above set of points in profit function to find optimal profit
Put all the points in
For
For
For
For
For
Conclusion:
For crop A optimal number of acres is 60
For crop B optimal number of acres is 90
Optimal profit is $33150
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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