Wal-Mart, a discount store chain, is planning to build a new store in

Question

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.

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.

Answer 1

Maximize: 4.25x + 5.10y + 4.50z + 5.20w + 4.10u + 4.90v + 3.80t

Subject to:
x + y + z ≥ 15000
x + y + z ≤ 140000
w + u + v ≤ 140000
w + u + v ≥ 15000
x + y + z ≤ 0.2(140000)
w + u + v ≤ 0.1(140000)
x, y, z, w, u, v, t ≥ 0