For example product P consists of two subassemblies. To manufacture
the first subassembly, one unit of RM1 passes through machine
A for 15 minutes. The output of machine A is moved to machine
C where it is processed for 10 minutes. The second subassembly
starts with RM2 processed in machine B for 15 minutes. The output
is taken to machine C for 5 minutes of processing. The two subassemblies
are joined with a purchased part in machine D. The result is
a finished unit of P. Product Q is manufactured by a similar
process as indicated in the figure.
The rectangle at the upper left indicates that one machine
of each type is available. Each machine operates for 2400 minutes
per week. OE stands for operating expenses. For this case the
operating expenses, not including the raw material cost is $6000.
This amount is expended regardless of amounts of P and Q produced.
Our problems include the following: Find the product mix that
maximizes profit. Identify the bottlenecks. For each product,
find the range over which the unit profit can change without
affecting the product mix. For each machine, identify the marginal
benefit of adding one more minute of machine time. For each
machine, find the range over which the time availability can
change without affecting the identity of the bottleneck.