Question

A real estate developer is planning to build an apartment building specifically for undergraduate students on a parcel of land adjacent to GMU. Four types of apartments can be included in the building: efficiencies, and one, two, and three bedroom units. Each efficiency requires 500 square feet; each one bedroom unit requires 700 square feet; each two bedroom unit requires 800 square feet; and each three bedroom unit requires 1,000 square feet. The developer believes that the building should include no more than 15 one bedroom units, 22 two bedroom units, and 10 three bedroom units. Local zoning ordinances do not allow the developer to build more than 40 units in a particular building location, and restrict the building to a maximum of 40,000 square feet. The developer has already agreed to lease 5 one bedroom units and 8 two bedroom units to a local rental agency. Market studies indicate that efficiencies can rent for $350/month, one bedroom units can rent for $450/month, two bedroom units can rent for $550/month, and three bedroom units can rent for $750/month. How many units of each type should the developer build to maximize revenue?

Answer 1

To maximize revenue, the developer should build 2 efficiency units, 5 one bedroom units, 8 two bedroom units and 25 three bedroom units

Explanation:

The Local zoning ordinances do not permit the developer to build more than 40 units in a particular building, and restrict the building to a maximum of 40,000 square feet.

The developer has already agreed to lease 5 one bedroom units and 8 two bedroom units to a local rental agency. In order not to exceed 40 units, the developer has 27 more units to building. If he builds 25 three bedroom units and two efficiency units, the number of units totals 4 and the area of the building totals 35,900 square feet.

Maximum revenue = (5×$450) + (8×$550) + (25×$1000) + (2×$350) = $26,100/month