A Total Integer Model Example

The owner of a machine shop is planning to expand by purchasing some new

machines – presses and lathes.  The owner has estimated that each press purchased will increase profit by \$100 per day and each lathe will increase profit by \$150 daily.  The number of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop.  The machine purchase prices and space requirements are as follows.

Machine

Required

Floor Space (ft2)

Purchase Price

Press

Lathe

15

30

\$8,000

4,000

The owner has a budget of \$40,000 for purchasing machines and 200 square feet of available floor space.  The owner wants to know how many of each type of machine to purchase in order to maximize the daily increase in profit.

The linear programming model for an integer programming problem is formulated in exactly the same way as the linear programming examples we have already done.  The only difference is that in this problem, the decision variables are restricted to integer values because the owner cannot purchase a fraction, or portion, of a machine.  The linear programming model follows.

maximize Z = \$100x1 + 150x2

subject to

8,000x1 + 4,000x2 < \$40,000

15x1 +      30x2 < 200 ft2

x1, x2 > 0 and integer

where

x1 = number of presses

x2 = number of lathes