1. Frank Hurley is a farmer in Ames, Iowa. He has 300 acres on which he wishes t
ID: 2779586 • Letter: 1
Question
1. 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?
Explanation / Answer
Case 1 - Frank Participate in program
Wheat Corn Total
Ratio 50 50 100
Land 150 150 300
Earning Rate (per acrea) $150 $200
Total Revenue $22,500 $ 30,000 $ 52,500
(Note - AS it is given that in program both crop should be planted in equal rate so consider ratio as 50:50)
Case 2 - Frank NOT Participate in program
Wheat Corn Total
Ratio 33.33% 66.67% 100
Land 100 200 300
Earning Rate (per acrea) $120 $195
Total Revenue $12,000 $ 39,000 $ 51,000
(Note - As mentioned that he must plant at least 100 acres of either crop, we consider planted wheat in 100 acres and remaining corn as it has high price)
AS by participating in Gov. Program, he will earn more by $2,500 comparing to NOT participating.
So It is suggested that He should Participate in Program.
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