(solution) Case-7 (10/21/2015) Part 1 (35 points) Tom's Mall has 10,000

(solution) Case-7 (10/21/2015) Part 1 (35 points) Tom's Mall has 10,000

Case-7 (10/21/2015)

Part 1 (35 points)

Tom?s Mall has 10,000 square feet of space to rent and wants to determine the types of stores that should occupy the mall.  The minimum number and maximum number of each type of store (along with the square footage of each type) are given in the Table 1.  The annual profit made by each type of store depends on how many stores of that type are in the mall.  This dependence is also given in the Table 2 (where all profits are in units of $10,000).  For example, if two department stores are in the mall, each department store will earn $210,000 profit per year.  Each store pays 5% of its annual profit as rent to Tom?s.  Determine how Tom can maximize its rental income from the mall.

Table 1:  

Store type

Square footage

Minimum

Maximum

Jewelry

500

1

3

Shoe

600

1

3

Department

1500

1

3

Book

700

0

3

Clothing

900

1

3

Table 2:

Profit per store (in $10,000s) if this many in mall

Store type

1

2

3

Jewelry

9

8

7

Shoe

10

9

5

Department

27

21

20

Book

16

9

7

Clothing

17

13

10

  • Define the decision variables. (6 points)
  • Define the objective functions. (6 points)
  • Define the constraints.(13 points)
  • Determine an optimal solution. (10 points)

Store Type
Jewelry
Shoe
Department
Book
Clothing Number Minimum
3
1
3
1
3 Maximum
1
1
1
0
1
Total Profit
Store Type
Jewelry
Shoe
Department
Book
Clothing Square footage
3
1500
3
600
3
4500
3
700
3
2700
10000 0 1
2
90,000.00 80,000.00
100,000.00 90,000.00
270,000.00 210,000.00
0 160,000.00 90,000.00
170,000.00 130,000.00 3
70,000.00
50,000.00
200,000.00
70,000.00
100,000.00 Used
70,000.00
100,000.00
200,000.00
160,000.00
100,000.00 3
10500
7500
30000
10500
15000 Used
10500
5000
30000
8000
15000
68500 Rent Fee
0
Jewelry
Shoe
Department
Book
Clothing 0 1
4500
5000
13500
8000
8500 2
8000
9000
21000
9000
13000
Total Constraints
Square footage
10000 <=
Number of stores
1 <=
1 <=
1 <=
0 <=
1 <= 10000 3 <=
1 <=
3 <=
1 <=
3 <= 3
3
3
3
3