Wal-Mart, a discount store chain, is planning to build a new store in Rock Springs, Maryland.. The parcel of land the company owns is large enough to accommodate a store with 140,000 square feet of floor space. Based on marketing and demographic surveys of the area and historical data from its other stores, Wal-Mart estimates its annual profit contribution per square foot for each of the store's departments to be as shown in the following table.
|
Department
|
Profit contribution per ft2
|
|
Men's clothing
|
$4.25
|
|
Women's clothing
|
5.10
|
|
Children's clothing
|
4.50
|
|
Toys
|
5.20
|
|
Housewares
|
4.10
|
|
Electronics
|
4.90
|
|
Auto supplies
|
3.80
|
Each department must have at least 15,000 ft2 of floor space and no department can have more than 20% of the total retail floor space. Men's women's and children's clothing plus housewares keep all their stock on the retail floor; however, toys, electronics, and auto supplies keep some items (bicycles, televisions, tires, etc.) in inventory. Thus, 10% of the total retail floor space devoted to these three departments must be set aside outside the retail area for stocking inventory.
a. Formulate a linear programming model that can be used to determine the floor space that should be devoted to each department in order to maximize profit contribution.
b. Determine the optimal floor space allocation and the resulting total contribution to profit.
c. Wal-Mart is considering the purchase of a parcel of land adjacent to this planned building site. The cost of the parcel is $190,000 and it would enable Wal-Mart to increase the size of the store to 160,000 ft2. Company policy requires that acquisitions of new land for expansion be offset by additional contribution to profit within five years. Historically, however, profit contributions decline in all departments by 10% if a store size increases past 150,000 ft2 (slower stock turnover, increased inventory costs, etc). Provide a justified recommendation with respect to this expansion option.