Optimal Resource Utilization

Generic Situation:

A manufacturer produces a number of products which use many of the same resources. He would like to build that mix of products that will insure a maximum profit, given his present inventory of resources.

Example:

Swen Swenson, owner of Swenson Saunas, sells two models of personal saunas, the Viking and the Eric the Red. Both models use 1 unit of the same commercially available standard steam generator. The Viking requires 9 hours of labor and 12 units of redwood, and the Eric the Red 6 hours of labor and 16 units of redwood. Each Viking sold generates a profit of $350 and each Eric the Red a profit of $300. Swen is starting a new production year with the following available resources: 200 steam generators, 1566 hours of labor, and 2880 units of redwood. Swen would like to know how many of each model to build in order to generate the highest profit given his resources ?

Profit Maximizing Solution:

If Swen produces 122 Viking units and 78 Eric the Red units, he will insure himself the maximum profit possible, given his present resources. - No other combination of units will produce a higher profit.