1) A professional football player is retiring, and he is thinking about going into the insurance business. He plans to sell four types of policies— homeowner’s insurance, auto insurance, boat insurance and life insurance. The average amount of profit returned per year by each type of insurance policy is as follows:
PLEASE TYPE ALL ANSWERS - PLEASE NO WRITTEN ANSWERS
Policy Yearly Profit/Policy
Each homeowner’s policy will cost $25, each auto policy will cost $18.50, each boat policy will cost $18 and each life insurance policy will cost $32 to sell and maintain. He has a budget of $80,000 per year. In addition, the sale of a homeowner’s policy will require 6 hours of effort; the sale of an auto policy will require 3.2 hours of effort, the sale of a boat policy will require 4 hours of effort and the sale of a life insurance policy will require 10 hours of effort. There are a total of 25,000 hours of working time available per year from himself and his employees.
He wants to sell at least twice as many auto policies as homeowner’s policies.
Formulate a linear programming model to maximize his profit by determining
(a) The decision variables.
(b) The objective function. What does it represent?
(c) All the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
Maximize z = xx x