Question

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 year by each type of insurance policy is as follows:

Policy                            Yearly Profit/Policy

Homeowner’s               $50

Auto 40

Life 75

Each homeowner’s policy will cost $18.20, each auto policy will cost $14.50 and each life insurance policy will cost $30.50 to sell and maintain. He has projected a budget of $80,000 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 function. 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

Decision variables
Let
x be the number of homeowner insurance policy to be sold
y be the number of auto insurance policy to be sold
z be the number of life insurance policy to be sold

Objective function
Maximize 50x + 40y+75z

Constraints

Sell and maintenance constraints
18.20x + 14.5y + 30.50z <=80000

Effort and time constraint
6.5x +3.7y+10z <=28000

Selling constraints
y = 2x

Non negative constraints

x,y,z>=0