Discuss the problem:
Q: 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.
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Final
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Reduced
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Objective
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Allowable
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Allowable
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Cell
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Name
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Value
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Cost
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Coefficient
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Increase
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Decrease
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$C$13
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Efficiencies Built
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0
|
-100
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350
|
100
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1E+30
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$C$14
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1-Bedroom Built
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8
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0
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450
|
100
|
100
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|
$C$15
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2-Bedroom Built
|
22
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0
|
550
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1E+30
|
100
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$C$16
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3-Bedroom Built
|
10
|
0
|
750
|
1E+30
|
300
|
|
|
|
|
|
|
|
|
|
|
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Final
|
Shadow
|
Constraint
|
Allowable
|
Allowable
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Cell
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Name
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Value
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Price
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R.H. Side
|
Increase
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Decrease
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$E$21
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Max # of Efficiencies
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0
|
0
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40
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1E+30
|
40
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$E$22
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Max # of 1-Bedroom
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8
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0
|
15
|
1E+30
|
7
|
|
$E$23
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Max # of 2-Bedroom
|
22
|
100
|
22
|
3
|
7
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|
$E$24
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Max # of 3-Bedroom
|
10
|
300
|
10
|
3
|
7
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$E$21
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Min # of Efficiencies
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0
|
-100
|
0
|
3
|
0
|
|
$E$22
|
Min # of 1-Bedroom
|
8
|
0
|
5
|
3
|
1E+30
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|
$E$23
|
Min # of 2-Bedroom
|
22
|
0
|
8
|
14
|
1E+30
|
|
$E$24
|
Min # of 3-Bedroom
|
10
|
0
|
0
|
10
|
1E+30
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|
$C$25
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Max Square Footage
|
33200
|
0
|
40000
|
1E+30
|
6800
|
|
$C$26
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Max # of Units
|
40
|
450
|
40
|
7
|
3
|
a. What is the optimal solution to this problem?
b. If the developer built one efficiency unit, what effect does this have on the total potential rental income? Justify your answer.
c. 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.
d. 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?