Question

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 Cape Cod is projected to be $5100, whereas that of a Ranch Home is projected at $5000.

​a)​Formulate the problem to maximize profit.

​For parts b) and c) below, can you determine the answer without resolving the problems with Solver?

​b)​A gentleman who owns 15 vacant lots adjacent to Judson’s 100 lots needs some money quickly and offers to sell his 15 lots (as a package deal) for $60,000. Should Judson buy? What assumptions are you making?

​c)​One of Judson’s salesmen 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?

Answer 1

a)

Let, Number of Cape cod to be built = x1

Number of Ranch Home to be built = x2

Objective function = maximize profit contribution = Max 5100x1 + 5000x2

Subject to,

x1 + x2<= 100 (Number of lots available)

200x1+100x2 <= 12000 (Carpentry hours constraint)

50x1+120x2 <= 13000 (Bricklayer labour hours constraint)

x1,x2 >= 0 (Non-negativity constraint)

Solving in excel solver we get,

Number of Cape cod to be built = x1 = 20

Number of Ranch Home to be built = x2 = 80

Maximized profit = 502000

Solver screenshot

Sensitivity report

Yes, Answers of part b) and c) can be determined from sensitivity report itself i.e without resolving the problems in solver

b)

From sensitivity report we can see shadow price of number of plots to be made house upon is 4900 and allowable increase up to 12.63157895. So Judson can have profit of 4900 per unit up to 12.63157895 plots

We can see, increase in profit => 4900*12.63157895 = 61894.73686 is greater than Cost Judson has to pay = $60,000 so, Judson can buy the extra 15 lots

Assumptions : Carpentry hours and BrickLayer hours will remain same

c) Even if Judson's salesman increases the profit contribution of Cape cods by $2000 it would not affect Judson's planned mix of homes as increase of $2000 is within allowable increase limit of $4900 for cape cods

Inherent Assumptions : All other variables remaining same while increasing profit contribution of cape cods