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Farmer Brown is planning his annual planting, and he grows two crops: corn and wheat. He has 100 acres of land available, and will be able to devote 150 days of labor to his crops. An acre of wheat requires four days of labor to plant and cultivate while an acre of corn requires only one day. He has $1000 of capital that he spend on the start-up costs of planting and cultivating. It costs $10 an acre to plant and cultivate corn, while the corresponding costs for wheat are $20 an acre. He expects a revenue of $40 per acre for the corn, and $120 an acre for wheat.

Farmer Brown receives an offer for a loan of up to $1,500: for each dollar borrowed, he will owe $1.035 to repay it. He also has been told he can rent an unlimited amount of land from his neighbor, Farmer Monsantoh, for $20 an acre, and he could hire extra help for $25 per day of labor.

a. Factoring the cost of the loan into the revenue, formulate an LO-model to determine how many acres of each Farmer Brown should plant as well as how much Farmer Brown should borrow, and how the loan should be spent, in order to maximize revenue. Clearly identify what your variables represent.

b. Solve the LO-model you found in part a.: you only need to provide your final, optimal tableau, and clearly state the optimal values of the variables.

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