Linear programming problem Formulation ,sensitivity analysis

Exercise 1: Hartman Company

Hartman Company is trying to determine how much of each of two products should be produced over the coming planning period. The only serious constraints involve labor availability in three departments. Shown below is information concerning labor availability, labor utilization and product profitability.

Product 1 Product 2 Labor available
Profit/unit $ 30.00 $15.00
Dept A hours/unit 1.00 0.35 100 hours
Dept B hours/unit 0.30 0.20 36 hours
Dept C hours/unit 0.20 0.50 50 hours

a) Develop a linear programming model for the problem and solve it to determine the optimal production quantities of products 1 and 2.

b) Suppose overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime? How much would you be willing to pay per hour of overtime in each department?

c) Suppose that 10, 6 and 8 hours of overtime may be scheduled in departments A,B, and C, respectively. The cost per hour of overtime is $18 in department A, $22.50 in department B, and $12 in department C. Revise the model and determine optimal product quantities if overtime is made available. What are the optimal production quantities, and what is the revised profit? How much overtime do you recommend using in each department ? What is the increase in profit if overtime is used?