Advising a building contractor
A building contractor has acquired a 10 acre site and plans to develop it as a residential area. The contractor has two basic designs for homes: a low income home and a middle income home. he expects to take 5 years to complete the project.
Low income homes cost 30,000 to build at a density of a 20 homes per acre, whereas middle income homes cost 40,000 to build at a density of 12 homes per acre. The contractor expects to sell a maximum of 100 low income homes and 75 middle income homes, but the zoning regulations will allow no more than a total of 155 homes on site. The local city council has also stipulated a formula to ensure that sufficient low income homes are constructed. This formula stipulates: the number of low income units shall be at least 35 units greater than half the number of middle income units. The contractor employs a work force of 60 people. The architect estimates that it will take a 2.0 labor years to build a low income home and a 2.5 labor years to build a medium income home.
The contractor expects to sell a low income home for 50,000 and a medium income home for 70,000. Your task is to advise the contractor. How many of each type of home should he build?