Carter Enterprises is involved in the soybean business in South Carolina, Alabama, and Georgia. The president of the company, Earl Carter, goes to a commodity sale once a month where he buys and sells soybeans in bulk. Carter uses a local warehouse for storing his soybean inventory. This warehouse charges $10 per average ton of soybeans stored per month (based on the average of the beginning and ending inventory each month). The warehouse guarantees Carter the capacity to store up to 400 tons of soybeans at the end of each month. Carter has estimated what he believes the price per ton of soybeans will be during each of the next six months. These prices are summarized in the following table. Month 1 2 3 4 5 6
Price per Ton $135 $110 $150 $175 $130 $145

Assume Carter currently has 70 tons of soybeans stored in the warehouse. How many tons of soybeans should Carter buy and sell during each of the next six months to maximize his profit trading soybeans?

Required:
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?