Frank Hurley is a farmer in Ames, Iowa.
He has 300 acres on which he wishes to plant wheat and corn for the season.
For crop rotation purposes he must plant at least 100 acres of each crop.
He can participate in a federal program that will require him to produce at least as much wheat as corn. Under this program, he is guaranteed to earn $150 per acre of wheat planted and $200 per acre of corn planted.
Alternatively he can opt not to participate in the program in which case he projects he would make only $120 per acre of wheat planted and $195 per acre of corn planted, but there would be no requirement to produce at least as much wheat as corn.
His goal is to maximize his total profit for the season.
a. If Frank did participate in the program
How many acres of wheat should he plant?
How many acres of corn should he plant?
What is his total expected profit?
b. If Frank did not participate in the program
How many acres of wheat should he plant?
What is his total expected profit?
How many acres of corn should he plant?
What would you recommend to Frank?