Question: Uncle Thad’s Farm grows corn, soy, and wheat. The farm sells its crops to two different distributers and at a local market. The farm has negotiated contracts with the two distributers for sale prices and minimum amounts of crop that the farm must deliver. The sale prices and minimum deliver amounts are given below.

The local market will buy at most 8 units of corn, 7 units of soy, and 4 units of wheat. The farm has 40 acres. Corn yields 3 units per acre, soy 6 units per acre, and wheat yields 4 units per acre. Due to crop rotation requirements, corn can be planted on at most 37.5% of the acres, soy on at most 37.5% of the acres, and wheat on at most 50% of the acres. How many acres of each crop should Uncle Thad plant in order to maximize revenues from sales? (It is okay to have a fractional number of acres for a crop. For instance, corn can be planted on 4.67 acres.)

(a) Formulate an LP to maximize revenue.

(b) Use LINDO to solve your model. How many acres of each crop should Uncle Thad plant?

(c) Uncle Thad is considering leasing 10 more acres at a cost of $10,000. Should Uncle Thad lease the land given that corn can be planted on at most 37.5% of the total acres, and wheat on at most 50% of the total acres?