Farmer Jack owns 140 acres of land. He is considering to plant two products: Cor

Question

Farmer Jack owns 140 acres of land. He is considering to plant two products: Corn and/or tomatoes.

Each acre of corn yields $460 profit, and each acre of tomatoes yields $320 profit.

Each acre of corn needs 0.025 labor and 1.2 tons of fertilizer.

Each acre of tomatoes needs 0.036 labor and 0.9 ton of fertilizer.

Farmer Jack has 40 tons of fertilizer and 12 labors available.

Formulate a linear programming model to determine how many acres of each crop to plant to maximize profit from his land. (Define the decision variables first, then formulate the problem).

Explanation / Answer

Decision Variables
How many acres of corn to plant ( x)
How many acres of tomatoes to plant (Y)

Formulate
Objective Function
Maximize Profit (P)
P = $460x + $320y

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