(1 pt) Your cousin Tom owns a 100 acre farm. In this climate he can grow corn, wheat, and soy. He wants you to help him determine how many acres he should use for each crop.

Assumptions

• All 100 acres will be used
• He will use a total of 1800 hours of labor
• His budget is $62,500.00
• It costs $650.00 per acre to grow corn
• It costs $525.00 per acre to grow wheat
• It costs $575.00 per acre to grow soy
• Each acre of corn requires 20 hours of labor
• Each acre of wheat requires 10 hours of labor
• Each acre of soy requires 14 hours of labor

Part A:

Set up a system of equations and solve this system, then use the solution to help Tom determine how to run the farm.
Note: The system of equation should be underdetermined, meaning it will have infinitely many solutions. Let t denote the number of acres of soy. Then

• Number of acres of corn: acres
• Number of acres of wheat: acres
• Number of acres of soy: acres

Part B:

Tom likely enjoys growing corn, so he wants to find the arrangement that involves the greatest number of acres of corn. Help him find this arrangement:

• Number of acres of corn: acres
• Number of acres of wheat: acres
• Number of acres of soy: acres

Part C:

Tom makes the largest profit from soy, so he wants you to help him figure out how to grow the greatest number of acres of soy. He stipulates that the arrangement should use all 100 acres, all 1800 hours of labor, and the entire $62,500.00 budget. Help him find this arrangement.

• Number of acres of corn: acres
• Number of acres of wheat: acres
• Number of acres of soy: acres

NOTE: Assume that Tom must use up all of his resources. He will be heavily fined if he leaves any of his land, labor, or budget unused.