To illustrate how linear programming can be used to identify the optimal mix with
multiple internally constrained resources, we will continue to use the Schaller Company
example. However, the example will be expanded to include a wider variety of constraints.
In addition to the constraints already identified, two more internal constraints
will be added. Assume that the two parts (X and Y) are produced in three sequential
processes: grinding, drilling, and polishing. The grinding process uses two machines
that provide a total of 80 grinding hours per week. Each part requires one hour of
grinding. The polishing process is labor intensive. This process provides 90 labor hours
per week. Part X uses two hours per unit, and Part Y uses one hour per unit. Information
on Schaller’s constraints is summarized in Exhibit 21-8. As before, the objective
is to maximize Schaller’s total contribution margin subject to the constraints faced
by Schaller.