Reformulating Farmer Jones’s LP:

From the given scenario, it is observed that farmer Jones must determine the number of corn and wheat to plant this year.

Let us consider,

x1 is the variable to represent the number of bushels of corn produced.

x2 is the variable to represent the number of bushels of corn produced.

Wheat can be sold at $4 a bushel and corn can be sold at $3 a bushel.

The object of the farmer is to maximize the total revenue from wheat and corn.

The objective function is as follows:

Maximize z = 3x1+4x2

Considering the constraints,

Constraint 1: Seven acres of land is available.

Constraint 2: 40 hours of labor are available each week.

Constraint 3: At least 30 bushels of corn must be produced.

Expressing the constraint 1 in terms of x1 and x2:

{(1/10 acers of land produces 1 bushel of corn)×(number of bushels of corn produced)+(1/25 acers of land produces 1 bushel of wheat)×(number of bushels of wheat produced)}≤7

x110+x225≤7

Expressing the constraint 2 in terms of x1 and x2:

{

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Chapter 3.1, Problem 2P

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