Question

An industrial machinery manufacturer produces shapers and drill presses. The manufacturer fore-casts that the demand for shapers for the next month will be at least 5 and the demand for drill presses for the next month will be at most 7. A shaper earns a profit of €40,000 and a drill press, €50,000. Both the shaper and the drill press use few common components like belts, electric motors, hydraulic drives, sensors, etc. A shaper needs 15 units of such common components and a drill press, 18 units. The store has 200 units of the components in stock. The cost of other parts is allocated from a common budget. A shaper needs €12,000 and a drill press needs €16,000 from the budget. The manufacturer has a budget of €150,000. The manufacturer wants to determine the number of shapers and drill presses to produce to maximize its profits. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer.

Answer 1

Solution:

Let us define the variables.

x1 = number of shaper units
x2 = number of drill press units.

Objective function:

To maximize profits.

Z = 40000x1 + 50000x2

Subject to constraints,

x1 >= 5

x2 <= 7

15x1 + 18x2 <= 200

12000x1 + 16000x2 <= 150000

x1, x2 >= 0 and integers.

The complete solution to the above problem is given below,