Question

A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers and requires two tons of fertilizer. Each acre planted with corn yields $3000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available. The farmer wants to maximize his profit from planting his land. a) Write the managerial formulation for the farmer’s problem. b) Use Solver to determine the plan that maximizes the farmer’s profit. c) If additional fertilizer became available at 600$/ton, should the farmer purchase any? (Hint: You need to generate the sensitivity report to answer that)

Answer 1

a) b)

X1 = acre of land planted with wheat

X2 = acre of land planted with corn

c)

Shadow price is the maximum price one is willing to pay for an additional unit of a given limited resource. As shadow price for fertilizer is 625$/ton whereas fertilizer is available at 600$/ton, the farmer should purchase fertilizer. Although in the given case as all the available workers are being utilized, additional unit of fertilizer would not help in maximizing profit.