Manufacture (in-house) vs. Buy (outsource)

Generic Situation:

A manufacturer receives an order for several of his products that he cannot entirely fill given his present production commitments. In such a case the owner must decide which items to produce in-house and which to outsource to other manufacturers.

Example:

Carter Wallace of Gromits Inc. has just received a $750,000 order from his best client for various quantities of three models of gromits summarized below.



Model AModel BModel C
Number Ordered3,0002,000900
Stamping hours/unit21.53
Assembly hours/unit121
GROMIT ORDER


Unfortunately at the moment Gromits Inc. has a very heavy schedule and can only spare 10,000 hours of stamping and 5,00 hours of assembly although the entire order will require 11,700 hours of stamping and 7,900 hours of assembly. Naturally Mr. Wallace wants to fill this order for his most profitable client. He would also like to make the highest profit possible taking into account that he must outsource some of the work. The cost of making models A, B and C in house are $50, $83, and $130 respectively; the costs to subcontract are $61, $97, and $144 respectively. Carter wants to determine what combination of in-house and subcontracting will ensure him an optimal profit.

Profit Maximizing Solution:

Gromits Inc. should manufacture the following number in-house: 3,000 Model A's, 550 Model B's, and 900 Model C's. It should subcontract for 1450 Model B's. No other combination of in-house manufacture and outsourcing will produce a higher profit for this particular order.