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?