The Judson Corporation has acquired 100 lots on which it is about to build homes. Two styles of homes are to be built, the "Cape Cod" and the "Ranch home". Judson wishes to build these 100 homes over the next nine months. During this time, Judson will have available 13,000 man-hours of bricklayer labor and 12,000 hours of carpenter labor. Each Cape Cod requires 200 man-hours of carpentry labor and 50 man-hours of bricklayer labor. Each Ranch Home requires 120 hours of bricklayer labor and 100 man-hours of carpentry. The profit contribution of a Cape Cod is projected to be $5,100, whereas that of a Ranch Home is projected at $5,000. When formulated as an LP and solved, the problem is as follows:

Ranges in which the basis is unchanged:

(a) A gentleman who owns 15 vacant lots adjacent to Judson's 100 lots needs some money quickly and offers to sell his 15 lots for $60,000. Should Judson buy? What assumptions are you making?
(b) One of Judson's salesman who is a native of Massachusetts feels certain he could sell the Cape cods for $2000 more each than Judson is currently projecting. Should Judson change its planned mix of homes? What assumptions are inherent in your recommendation?

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MAX = 5100 * C + 5000 * R; R < 100; 200 * C + 100 * R < 12000; 50 *C + 120 * R < 13000; %3D Optimal solution found at step: Objective value: 502000.0 Reduced Cost 0.0000000 Variable Value 20.00000 80.00000 Slack or Surplus R 0.0000000 Dual Price Row 1.000000 2 3 4 0.0000000 0.0000000 2400.000 0.0000000