Iggy Olweski, a professional football player, is retiring, and he is thinking about going into the insurance business. He plans to sell three types of policies—homeowner’s insurance, auto insurance, and life insurance. The average amount of profit returned per year by each type of insurance policy is as follows:
Policy Yearly Profit/Policy
Homeowner’s ... $35
Auto ........ 20
Life ......... 58

Each homeowner’s policy will cost $14 to sell and maintain; each auto policy, $12; and each life insurance policy, $35. Iggy has projected a budget of $35,000 per year. In addition, the sale of a homeowner’s policy will require 6 hours of effort; the sale of an auto policy, 3 hours; and the sale of a life insurance policy, 12 hours. Based on the number of working hours he and several employees could contribute, Iggy has estimated that he would have available 20,000 hours per year. Iggy wants to know how many of each type of insurance policy he would have to sell each year in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.