The actual problems and instructions are found in the word document, and the excel template is already made, which is the excel file.

The actual problems and instructions are found in the word document, and the excel template is already made, which is the excel file.

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Business Management 2321 – Practical Exercise #3 DO NOT SUBMIT THIS PAGE WITH YOUR EXERCISE Goal Programming You have decided to invest in off-campus…

The actual problems and instructions are found in the word document, and the excel template is already made, which is the excel file.

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Mark Chri stobek.1
Business Management 2321 – Practical Exercise #3
DO NOT SUBMIT THIS PAGE WITH YOUR EXERCISE
Goal Programming
You have decided to invest in off-campus student housing in a college in a town close to their retirement homes in South
Florida. You will have to make 20% down payments on the apartment complexes since mortgage companies will only
finance 80% of the purchase price (at an annual percentage rate of 5.75%).
Monthly expenses (maintenance, insurance,
and utilities) are estimated to 4% of the purchase price.
Florida laws require that each off-campus apartment houses only one student per bedroom.
Since there is a strong
demand for student housing, assume that all of the apartments will be rented.
Apartment Type
Monthly Rental per Student
Monthly Rental per Apartment
One Bedroom
$1,200
$1,200
Two Bedroom
$900
$1,800
Three Bedroom
$550
$1,650
There are 10 apartment complexes available.
The pertinent information on each apartment complex is shown in the table
below:
Apartment Complexes
A
B
C
D
E
F
G
H
I
J
Price
$400,000
$600,000
$500,000
$700,000
$350,000
$450,000
$650,000
$550,000
$750,000
$350,000
Down
Payment
$80,000
$120,000
$100,000
$140,000
$70,000
$90,000
$130,000
$110,000
$150,000
$70,000
Monthly
Expenses
$17,868
$26,802
$22,335
$31,269
$15,635
$20,101
$29,035
$24,568
$33.502
$15,635
One-
Bedroom
6
8
4
4
0
10
6
6
8
12
Rental
Income
$7,200
$9,600
$4,800
$4,800
$0
$12,000
$7,200
$7,200
$9,600
$14,400
Two-
Bedroom
4
8
6
13
10
0
8
6
8
2
Rental
Income
$7,200
$14,400
$10,800
$23,400
$18,000
$0
$14,400
$10,800
$14,400
$3,600
Three-
Bedroom
3
4
6
4
0
6
6
6
8
0
Rental
Income
$4,950
$6,600
$9,900
$6,600
$0
$9,900
$9,900
$9,900
$13,200
$0
Total
Apartment
s
13
20
16
21
10
16
20
18
24
14
Total
Income
$19,350
$30,600
$25,500
$34,800
$18,000
$21,900
$31,500
$27,900
$37,200
$18,000
Monthly
Profit
$1,482
$3,798
$3,165
$3,531
$2,365
$1,799
$2,465
$3,332
$3,698
$2,365

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Mark Chri stobek.1
Business Management 2321 – Practical Exercise #3
DO NOT SUBMIT THIS PAGE WITH YOUR EXERCISE
You have the following constraints that cannot be violated.
The total monthly rent from the one-bedroom apartments cannot exceed 45% of the total monthly rent.
The total monthly rent from the two-bedroom apartments cannot exceed 40% of the total monthly rent.
The total monthly rent from the three-bedroom apartments cannot exceed 35% of the total monthly rent.
The total number of apartments cannot exceed 120.
You ran a linear program with binary decision variables (1 for “Buy”, 0 for “Don’t Buy”).
There was an optimal solution that
would satisfy all of the constraints simultaneously with all decision variables for the apartment complexes being binary.
After researching the rental market near the college and surveying the present students, you have established the
following goals for your model:
Goal 1:
The total of the down payments cannot exceed $1,000,000.
Goal 2:
No less than 30 one-bedroom apartments.
Goal 3:
No more than 55 one-bedroom apartments.
Goal 4:
No less than 25 two-bedroom apartments.
Goal 5:
No more than 50 two-bedroom apartments.
Goal 6:
No more than 30 three-bedroom apartments.
Goal 7:
Total monthly profit is at least
$25,000.
However, when the 7 goals were added into the linear program, the problem was infeasible.
Procedure:
Download the EXCEL spreadsheet from Carmen.
On the “Linear Programming (1)” tab, replicate the linear program with binary variables.
The objective function should be
to maximize the profit.
Confirm that the model has a solution with all of the decision variables being binary.
On the “Linear Programming (2)” tab, modify the linear program to include constraints for the 7 goals. The objective
function should be to maximize the profit.
Prove that the model is infeasible with all of the decision variables being binary
(some of the binary decision variables will have non-binary values in the solution – this is OK).
On the “Goal Programming” tab, modify the linear program with the 7 goals by changing it into a goal program with 14
deviation variables.
Prove that the model has a solution with all of the decision variables being binary (do not constrain
the deviation variable to be binary).
The objective function should be to minimize the percent deviation (the objective
function coefficients for the decision variables will be zero).
The RHS Values for the One-Bedroom Rent constraint, the Two-Bedroom Rent constraint, and
the Three-Bedroom Rent constraint in all of the spreadsheets are set to zero.
Do not change
the value of the RHS for these constraints.

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A
B
C
D
Solution
Maximize
One-Bedroom Rent
Two-Bedroom Rent
Three-Bedroom Rent
Total Apartments
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E
F
G
H
I
J

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