Reference no: EM132228304
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-, and three-bedroom units. Each efficiency requires 550 square feet; each one-bedroom apartment requires 725 square feet; each two-bedroom apartment requires 850 square feet; and each three-bedroom unit requires 1,025 square feet. The developer believes that the building should include no more than 16 one-bedroom units, 20 two-bedroom units and 12 three-bedroom units. Local zoning ordinances do not allow the developer to build more than 40 units in this particular building location, and restrict the building to a maximum of 42,000 square feet. The developer has already 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 $560 per month, one bedrooms for $675 per month, two-bedrooms for $750 per month and three-bedrooms for $970 per month. The developer wants to know how many units of each type should be included in the building plans in order to maximize the potential rental income from the building?
1. Explain this model in clear terms: what are the decision variables, what is the objective function, what are the constraints, etc? You can write out the algebraic formulation, but be sure to provide a contextual explanation as well, so that someone unfamiliar with optimization could still understand the model.
2. Build a spreadsheet model that implements the model you outlined in question 1. Find the optimal solution using Solver.
(A) Answer the following questions about your optimal solution.
How many of each type of housing unit should be included (fractions are allowed)?
What is the maximum total rental income possible?
Which constraint(s) are binding?
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