Question

4. An insurance agent plans to sell three types of policies- homeowner's insurance, auto insurance and life insurance. The average amount of profit returned per vear by each type of insurance policy is as follows: Policy Homeowner's Auto Life Yearly Profit/Policy $50 40 75 Each homeowner's policy will cost $18.20, each auto policy will cost S14.50 and each life insurance policy will cost $30.50 to sell and maintain. He has projected a budget of S80,000 per year. In addition, the sale of a homeowner's policy will require 6.5 hours of effort; the sale of an auto policy will require 3.7 hours of effort and the sale of a life insurance policy will require 10.5 hours of effort. There are a total of 28,000 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 that meets these restrictions and maximizes total yearly profit for the agent (a) Define the decision variables. (b) Determine the objective funn. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents Note: Do NOT solve the problem after formulating

Answer 1

(a)

x = Number of homeowner's policies

y = Number of auto policies

z = Number of life policies

P = Yearly profit ($)

(b)

Maximize P = 50x + 40y + 75z

(c)

18.20x + 14.50y + 30.50z ≤ 80000 [Cost budget]

6.5x + 3.7y + 10.5z ≤ 28000 [Hours of working time]

x, y, z ≥ 0 and integers

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