Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 12

Lawns Unlimited is a lawn care and maintenance company. One of its services is to seed new lawns as well as bare or damaged areas in established lawns. The company uses three basic grass seed mixes it calls Home 1, Home 2, and Commercial 3. It uses three kinds of grass seed-tall fescue, mustang fescue, and bluegrass. The requirements for each grass mix are as follows:
The company believes it needs to have at least 1,200 pounds of Home 1 mix, 900 pounds of Home 2 mix, and 2,400 pounds of Commercial 3 seed mix on hand. A pound of tall fescue costs the company $1.70, a pound of mustang fescue costs $2.80, and a pound of bluegrass costs $3.25. The company wants to know how many pounds of each type of grass seed to purchase to minimize cost.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.