A firm operates two farms of comparable productivity. Each farm has a certain am

Question

A firm operates two farms of comparable productivity. Each farm has a certain amount of usable acreage and a supply of labor hours to plant and tend the crops. Farm 1 has 600 acres and 2000 labor hours available per month. The corresponding figures are 800 acres and 2500 labor hours per month for Farm 2. The firm is considering two crops for planting: corn and peas. The maximum acreage that can be devoted to each crop is as follows: 900 acres for corn and 700 acres for peas. Corn requires 3 labor hours per acre per month, while peas require 5 labor hours per acre per month. The expected profits are $250 per acre for corn, and $350 per acre for peas. The firm needs to determine how many acres to devote to each crop on each farm. The objective is to maximize total profit. Formulate as a Linear Programming problem. Do not solve.

Explanation / Answer

Forming of Linear Programming Problem

Let X1 be the variable for corn and X2 the variable for peas.

Maximize,           250X1 + 350X2

Subject to constraints

900X1 + 700X2 < 1400

2700X1 + 3500X2 < 4500

X1 & X2 > 0

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