Question

Real Estate Development

A real estate developer plans to build an apartment building near a major university aimed at generating rental income from graduate students. Four types of apartment are being considered in the planning process: studio apartments and 1, 2 or 3-bedroom units. It is assumed that studio apartments will be 500 sq. ft., 1-bedroom units will be 700 sq. ft., 2-bedroom units will be 800 sq. ft. and 3-bedroom units will be 1,000 sq. ft.

The develop does not believe that the building should have more than 15 1-bedroom units, 20 2-bedroom unit and 5 3-bedroom units. Current zoning restrictions limit the building to 40,000 sq. ft. in total and no more than 45 residential units. A local temporary housing agency has invested in the project, on the condition that it can lease five 1-bedroom units and eight 2-bedroom units for its own clients.

Estimated market rents for apartments are: studio - $350/mo., 1-bedroom - $450/mo., 2-bedroom - $550/mo. and 3-bedroom - $750/mo.

1. Create a linear spreadsheet model to advise the developer on the optimal design.

2. What constraints are binding?

Answer 1

1) Let x_1, x_2, x_3, x₄ are number of units of studio apartments and 1, 2 or 3-bedroom units respectively.

Constraints to

500x₁+700x₂+800x₃+1000x₄< 40000 (Area constraint limited to 40000 sq. feet)

X₁<1

X₂< 15 (maximum number of units that can be constructed)

X₃< 20(maximum number of units that can be constructed)

X₄< 5(maximum number of units that can be constructed)

Objective function

Max Z=350x₁+450X₂+550X₃+750_X4

(Note: From this objective function we need to reduce the units which are giving on lease to developer to client to get the original profit)

2) Binding constraints

· Area is limited to 40000square feet

· Number of units that can be constructed is limited to 15,20,5 1, 2 or 3-bedroom units respectively.

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