A real estate developer has acquired 80 lots on which he is about to build homes. Two styles of homes are to be built, the "Town house" and the "Duplex". The developer wishes to build these 80 homes over the next 6 months. During this time, he will have available 11,000 man-hours of bricklayer labor and 10,000 hours of carpenter labor. Each Duplex requires 200 man-hours of carpentry labor and 50 man-hours of bricklayer labor. Each Town house requires 120 hours of bricklayer labor and 100 man-hours of carpentry. The profit contribution of Duplex is projected to be $5100, whereas that of a Town house is projected at $5000.

a) What is the mix of homes to maximize profit?

b) There are 20 vacant lots adjacent to the current developer available for sale for $70,000 (as a package). Should the developer buy them, and why? Please state any assumptions that you are making.

c) One of the salesmen who is a local resident feels certain he could sell the Duplexes for $5000 more each than what is currently projecting. Should the developer change his planned mix of homes? What assumptions are inherent in your recommendation?