For the following problem, solve the linear programming model by using the computer. You can use either QM for Windows or Solver (in Excel) to solve this problem.
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:
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 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.
Formulate a linear programming model for this problem.
Solve this model by using the computer.