A real estate developer is planning to build an apartment building specifically for grduate students on a parcel of land adjacent to a major university. 4 types of apartment can be included in the building : efficiencies(E), one bedroom(A), two-bedrrom(B), and three bedroom(C) units. each efficiency requires 700 square feet, each one-bedroom apartment 900 square feet, each two bedroom apartment 1100 square feet, and each three bedroom apartment 1300 square feet. The developer believes that the building should include no more than 14 0ne bedroom units, 23 two bedroom units and 11 three bedroom units.Local zoning ordinances (law) do not allow the developer more than 39 units in this particulad building location, and resrict the building to a maxim of 48,000 square feet. The developer has already agreed to lease 6 one bedroom units and 7 two bedroom units to a local rental agency that is a "silent partner' in this endeavor. (if the apartments are not provided the developer will go bankrupt. Therefore this units must be built) Markets studies indicate that efficiencies can be rented for 900 month, one bedroom for 1,100 per month, two bedroom for 1,300 per month and three bedroom for 1,700 per month. How many rental units of each type should the developer include in the building plans in order to maximize the potential rental income from the building ( assuming he can rent the entire building all of the time). Using mathematical symbol, formulate as a linear programming model a) define decision variables b) specify the objective function c) write the constraints ( using inequalities ) including tthe non negative statement.
Explain please