A farmer is considering planting some combinations of corn, soybeans, and rice. She has 10,000 acres of land available and 200,000 hours of labor. The following table details the profit, risk, pollution, and labor requirements (all per-acre) associated with each activity.
|
|
Corn
|
Soybeans
|
Rice
|
|
Revenue
|
350
|
525
|
400
|
|
Risk
|
75
|
90
|
65
|
|
Pollution
|
5
|
7
|
12
|
|
Land
|
1
|
1
|
1
|
|
Labor
|
20
|
17
|
15
|
Given that she wants to maximize profit and minimize risk and pollution:
a. Find the optimal feasible level for each goal independently, assuming that all of the land is used.
b. Find the optimal solution for a GP using the results from part a as target values, assuming that she places about two-thirds more emphasis on minimizing risk than on the other objectives.
c. Find the optimal solution for a preemptive GP assuming her first priority is risk, followed by revenue, then pollution.