Analyse the case below in regard with the linear programming technique

Question

A good example of how to use operations research analysis is to consider the plight of farmer Jones. He must decide how many acres of corn and wheat to plant this year. One acre of corn will yield 10 bushels, and will require four hours of labor per week, and it will sell at $3 per bushel. Wheat will sell at $4 a bushel, will need 10 hours of labor a week and will yield 25 bushels per acre.

Farmer Jones has seven acres of land and can only work 40 hours per week. The government states that he must produce at least 30 bushels of corn in the coming year.

How many acres of corn and wheat does Farmer Jones plant to maximize his revenue?

Answer 1

Let c := # acres corn and w := # acres wheat

The objective function is 3*10*c + 4*25*w = 30c + 100w. We are maximizing.

The coefficient of c is $3/bushel * 10 bushels/acre

The coefficient of w is $4/bushel * 25 bushels/acre

Constraints:

4c + 10w ≤ 40 (maximum # of work hrs is 40)

c + w ≤ 7 (acreage constraint)

c ≥ 30/10 (must plant at least 3 acres of corn to get the required 10 bushels

w ≥ 0

Solution: c = 3, w = 2.8, revenue = $370