A Farmer Is Planning His Spring Planting Formulate the LP for This Problem

A farmer is planning his spring planting.He has 20 acres on which he can plant a combination of Corn,Pumpkins and Beans.He wants to maximize his profit but there is a limited demand for each crop.Each crop also requires fertilizer and irrigation water which are in short supply.There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available.The following table summarizes the data for the problem.
$\begin{array}{l|clccc}&\text { Profit per } & \text { Yield per } & \text { Maximum } & \text { Irrigation } & \text { Fertilizer } \\\text { Crop }&\text { Acre } \$) & \text { Acre } 1 \mathrm{~b} \text { ) } & \text { Demand } \mathrm{lb} \text { ) } & \text { acre } \mathrm{ft}) & \text { pounds/acre) }\\\hline\text { Corn } & 2,100 & 21,000 & 200,000 & 2 & 500 \\\text { Pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300\end{array}$
Formulate the LP for this problem.

Correct Answer:

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Let ^X₁ ^{= aces of corn}
X₂ = acres of pumpkin
X₃ = ac...

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