Domar properties plc have a site covering 20,000m2 on which they wanted to build a mixed estate of 2- & 4-bedroom houses. The 2-bedroom houses will each occupy a plot of 60m2 and will be sold at a profit of $15,000. On average each will have two people owning 1.2 cars. The 4-bedroom houses will each occupy a plot of 300m2 and will be sold at a profit of $50,000. On average each will have 5 people owning between them 1.5 cars.
They anticipate that roads, verges, play areas and other communal facilities will occupy 40% of the total site. Water and sewage considerations mean that the total number of residents on the estate should not exceed 250. The local authority has told Domar that the road entrance is unsuitable for more than 120 cars to be based on the estate.
How many houses of each type should Domar build in order to maximize their profit and how much profit should they expect if they did so?