Reference no: EM132226419

Lawns Unlimited is a lawn care and maintenance company. One of its services is to seen new lawns as well as bare areas 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:

Mix                                                                    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 a 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 in order to minimize cost. Formulate a linear programming model for this problem and solve using a computer.