Question:

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 Home1, 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:

Mix requirements

Home 1: No more than 50% tall fescue

At least 20% mustang fescue

Home 2: At least 30% bluegrass

At least 30% mustang fescue

No more than 20% tall fescue

Commercial 3: At least 50% but no more than 70% tall fescue

At least 10% bluegrass

The company believes it needs to have 1200 pounds of home 1 mix, 900 pounds of home 2 mix, and 2400 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.

Provide model formulation and computer solution to distinguish if it is a maximization or minimization problem.