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- September 13, 2020
- By menge

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