Multi-question real estate linear programming problem. Complete with set-up, answer, limits and sensitivty report. Attachments in Excel and Word.

A real estate developer is planning to build an apartment building
specifically for graduate students on a patch of land adjacent to Arapet
College in Madrid, Arizona. Four types of units can be included in the
building: efficiencies, and one-, two-, and 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, no more than 22 two-bedroom units, and no more than
10 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 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 that is a “silent
partner” in this endeavor. Market studies indicate that efficiencies
can be rented for $350 per month, one-bedroom for $450 per month,
two-bedrooms for $550 per month, and three-bedrooms for $750 per month.


To determine the mix of apartment types to maximize the potential
rental income, the developer solved an appropriate linear programming
model and obtained the output given in the sensitivity report below.









    Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$C$13 Efficiencies Built 0 -100 350 100 1E+30

$C$14 1-Bedroom Built 8 0 450 100 100

$C$15 2-Bedroom Built 22 0 550 1E+30 100

$C$16 3-Bedroom Built 10 0 750 1E+30 300









    Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$E$21 Max # of Efficiencies 0 0 40 1E+30 40

$E$22 Max # of 1-Bedroom 8 0 15 1E+30 7

$E$23 Max # of 2-Bedroom 22 100 22 3 7

$E$24 Max # of 3-Bedroom 10 300 10 3 7

$E$21 Min # of Efficiencies 0 -100 0 3 0

$E$22 Min # of 1-Bedroom 8 0 5 3 1E+30

$E$23 Min # of 2-Bedroom 22 0 8 14 1E+30

$E$24 Min # of 3-Bedroom 10 0 0 10 1E+30

$C$25 Max Square Footage 33200 0 40000 1E+30 6800

$C$26 Max # of Units 40 450 40 7 3



What is the optimal solution to this problem?

If the developer built one efficiency unit, what effect does this have
on the total potential rental income? Justify your answer.

Given the solution associated with the sensitivity report above, explain
why the developer does not utilize the 40,000 square feet authorized by
the zoning ordinances.

By how much does the developer’s monthly potential rental income
increase if the zoning board allows the developer to build five more
units in the complex?