The contribution margin per unit of scarce resource can also be used to identify the
optimal product mix when a binding external constraint exists. For example, assume
the same internal constraint of 120 drilling hours, but also assume that Schaller can sell
at most 60 units of Part X and 100 units of Part Y. The internal constraint allows
Schaller to produce 120 units of Part X, but this is no longer a feasible choice because
only 60 units of X can be sold. Thus, we now have a binding external constraint—one
that affects the earlier decision to produce and sell only Part X. Since the contribution
per unit of scarce resource (machine hour) is $300 for Part X and $200 for Part Y, it
still makes sense to produce as much of Part X as possible before producing any of Part
Y. Schaller should first produce 60 units of Part X, using 60 machine hours. This leaves
60 machine hours, allowing the production of 20 units of Part Y. The optimal mix is
now 60 units of Part X and 20 units of Part Y, producing a total contribution margin
of $30,000 per week [($300 60) ($600 20)].