Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 44

The Goliath Tool and Machine Shop produces a single product that consists of three subcomponents that are assembled to form the product. The three components are manufactured in an operation that involves two lathes and three presses. The production time (in minutes per unit) for each machine for the three components is as follows:
The shop splits the lathe workload evenly between the two lathes, and it splits the press workload evenly among the three presses. In addition, the firm wishes to produce quantities of components that will balance the daily loading among lathes and presses so that, on the average, no machine is operated more than 1 hour per day longer than any other machine. Each machine operates 8 hours per day.
The firm also wishes to produce a quantity of components that will result in completely assembled products, without any partial assemblies (i.e., in-process inventories). The objective of the firm is to maximize the number of units of assembled product per day.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
c. The production policies established by the Goliath Tool and Machine Shop are relatively restrictive. If the company were to relax either its machine balancing requirement (that no machine be operated more than an hour longer than any other machine) or its restriction on inprocess inventory, which would have the greatest impact on production output What would be the impact if both requirements were relaxed