A real estate developer is planning to build an apartment building specifically for graduate students on a parcel of land adjacent to a major university. Four types of apartments can be included in the building: efficiencies, and one-, two-, or three-bedroom units. Each efficiency requires 500 square feet; each one-bedroom apartment requires 700 square feet; each two-bedroom apartment 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 this particular building location. They restrict the building to a maximum of 40,000 square feet. The developer already has agreed to lease 5 one-bedroom units and 8 two-bedroom units to a local rental agency that is a “silent partner” in this endeavor. Market studies indicate that efficiencies can be rented for $350 per month, one-bedrooms for $450 per month, two-bedrooms for $550 per month, and three-bedrooms for $750 per month. How many rental units of each type should the developer include in the building plans to maximize the potential rental income from the building?

a. Formulate an LP model for this problem.

b. Create a spreadsheet model for this problem and solve it using Solver.

c. What is the optimal solution?

d. Which constraint in this model limits the builder’s potential rental income from increasing any further?