A Farmer in Egypt Owns 50 Acres of Land

question 64

Essay

A farmer in Egypt owns 50 acres of land. He is going to plant each acre with cotton or corn. Each acre planted with cotton yields $400 profit; each with corn yields $200 profit. The labor and fertilizer used for each acre are given in the table below. Resources available include 150 workers and 200 tons of fertilizer.
-(A) Formulate a linear programming model that will enable the farmer to determine the number of acres that should be planted cotton and/or corn in order to maximize his profit.
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(B) Find an optimal solution to the model in (A) and determine the maximum profit.
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(C) Implement the model in (A) in Excel Solver and obtain an answer report. Which constraints are binding on the optimal solution?
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(D) Obtain a sensitivity report for the model in (A). How much should the farmer be willing to pay for an additional worker?
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(E) Suppose the farmer hires 10 additional workers. Can you use the sensitivity analysis obtained for (D) to determine his expected profit? Would his planting plan change? Explain your answer.
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(F) Suppose the farmer now wants to hire 20 additional workers, instead of just 10. Can you use the sensitivity analysis obtained for (D) to determine his expected profit? Explain your answer.

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Definitions:

TVC

Total Variable Costs, which are the costs that change with the level of production or service delivery.

MC

Refers to Marginal Cost, the extra cost incurred from producing one more unit of a good or service.

Profit-Maximizing

Profit-Maximizing refers to the point at which a firm achieves the highest possible profit through the manipulation of production or pricing strategies.

MR = MC

A condition in economics where marginal revenue equals marginal cost, often considered the point of profit maximization for firms in perfectly competitive markets.