Question

A company produces and sells 3 types of organic fertilizer. A pound of Brand 1 earns a profit of $3 per pound. Brand II earns a profit of $4 per pound, and Brand III earns a profit of $3 per pound. 1 pound of Brand I requires 3 pounds of raw material and takes 2 hours of labor to produce it. 1 pound of Brand II requires 4 pounds of raw material and takes 3 hours of labor to produce it. 1 pound of Brand III requires 2 pounds of raw material and takes 2 hours of labor to produce it. Each day the company has 250 pounds of raw materials to use and because of union rules must have at least 100 labor hours for its workers. In addition since Brand II is the most popular they need to produce at least 15 pounds of it.

How many pounds of each Brand of fertilizer should they produce each day to maximize their profit? And what is their profit?

Answer 1

Let brand 1 produces x pounds

brand 2 produces y pounds

Brand 3 produces z pounds

Constraints are

3x + 4y + 2z <= 250

2x + 3y + 2z >= 100

y >= 15

Objective function is

Maximize P = 3x + 4y + 3z

Solving by simplex method

Brand 1 = 0 pounds , Brand 2 = 15 pounds , Brand 3 = 95 pounds should be produced Maximum profit is $ 345