3-2. A small manufacturing operation produces six kinds of parts, using three machines. For the

coming month, a certain number of each part is needed, and a certain number of parts can be

accommodated on each machine; to complicate matters, it does not cost the same amount to make

the same part on different machines. Specifically, the costs and related values are as follows:

Part

Machine 1 2 3 4 5 6 Capacity

1 3 3 2 5 2 1 80

2 4 1 1 2 2 1 30

3 2 2 5 1 1 2 160

Required 10 40 60 20 20 30

(a) Using the model in Figure 3-1a, create a file of data statements for this problem; treat the

machines as the origins, and the parts as the destinations. How many of each part should be produced on each machine, so as to minimize total cost?

(b) If the capacity of machine 2 is increased to 50, the manufacturer may be able to reduce the total

cost of production somewhat. What small change to the model is necessary to analyze this situation? How much is the total cost reduced, and in what respects does the production plan change?

(c) Now suppose that the capacities are given in hours, rather than in numbers of parts, and that it

takes a somewhat different number of hours to make the same part on different machines:

Part

Machine 1 2 3 4 5 6 Capacity

1 1.3 1.3 1.2 1.5 1.2 1.1 50

2 1.4 1.1 1.1 1.2 1.2 1.1 90

3 1.2 1.2 1.5 1.1 1.1 1.2 175

Modify the supply constraint so that it limits total time of production at each origin rather than

the total quantity of production. How is the new optimal solution different? On which machines is

all available time used?

(d) Solve the preceding problem again, but with the objective function changed to minimize total

machine-hours rather than total cost.