Business (Linear Programming)
posted by JYD .
WalMart, 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, WalMart 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.
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.
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