a. In Problem 42, Mega-Mart is considering purchasing a parcel of land adjacent to the current site on which it plans to build its store. The cost of the parcel is $190,000, and it would enable Mega-Mart to increase the size of its store to 160,000 square feet. Discuss whether Mega-Mart should purchase the land and increase the planned size of the store. b. Suppose that the profit per square foot will decline in all departments by 20% if the store size increases to 160,000 square feet. (If the stock does not turn over as fast, increasing inventory costs will reduce profit.) How might this affect Mega-Mart's decision in (a)?

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Chapter2: Introduction To Spreadsheet Modeling
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a. In Problem 42, Mega-Mart is considering purchasing a parcel of land adjacent to the current
site on which it plans to build its store. The cost of the parcel is $190,000, and it would enable
Mega-Mart to increase the size of its store to 160,000 square feet. Discuss whether Mega-Mart
should purchase the land and increase the planned size of the store.
b. Suppose that the profit per square foot will decline in all departments by 20% if the store size
increases to 160,000 square feet. (If the stock does not turn over as fast, increasing inventory
costs will reduce profit.) How might this affect Mega-Mart's decision in (a)?
Transcribed Image Text:a. In Problem 42, Mega-Mart is considering purchasing a parcel of land adjacent to the current site on which it plans to build its store. The cost of the parcel is $190,000, and it would enable Mega-Mart to increase the size of its store to 160,000 square feet. Discuss whether Mega-Mart should purchase the land and increase the planned size of the store. b. Suppose that the profit per square foot will decline in all departments by 20% if the store size increases to 160,000 square feet. (If the stock does not turn over as fast, increasing inventory costs will reduce profit.) How might this affect Mega-Mart's decision in (a)?
Mega-Mart, a discount store chain, is to build a new store in Rock Springs. The parcel of land the
company has purchased 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, Mega-Mart estimates its annual profit per square foot for each of the store's departments
to be as shown in the following table.
Each department must have at least 15,000 square feet of floor space, and no department
can have more than 20% of the total retail floor space. Men's, women's, and children's cloth-
ing plus housewares keep all their stock on the retail floor; however, toys, electronics, and auto
supplies keep some items (such as bicycles, televisions, and tires) 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. Mega-Mart wants to know the floor space that should be devoted to each
department to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.
Department
Men's clothing
Women's clothing
Children's clothing
Toys
Housewares
Electronics
Auto supplies
Profit per ft.²
$4.25
5.10
4.50
5.20
4.10
4.90
3.80
Transcribed Image Text:Mega-Mart, a discount store chain, is to build a new store in Rock Springs. The parcel of land the company has purchased 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, Mega-Mart estimates its annual profit per square foot for each of the store's departments to be as shown in the following table. Each department must have at least 15,000 square feet of floor space, and no department can have more than 20% of the total retail floor space. Men's, women's, and children's cloth- ing plus housewares keep all their stock on the retail floor; however, toys, electronics, and auto supplies keep some items (such as bicycles, televisions, and tires) 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. Mega-Mart wants to know the floor space that should be devoted to each department to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using the computer. Department Men's clothing Women's clothing Children's clothing Toys Housewares Electronics Auto supplies Profit per ft.² $4.25 5.10 4.50 5.20 4.10 4.90 3.80
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