W-Mart W-Mart, a discount store chain, is to build a new store in Alabama. 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, W-Mart estimates its annual profit per square foot for each of the store's departments to be as shown in the table below. 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 clothing 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. W-Mart wants to know the floor space that should be devoted to each department in order to maximize profit. Department Men's clothing Women's clothing Children's clothing Toys Housewares Profit per square feet $4.25 5.10 4.50 5.20 4.10 4.90 Electronics Auto supplies 3.80
W-Mart W-Mart, a discount store chain, is to build a new store in Alabama. 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, W-Mart estimates its annual profit per square foot for each of the store's departments to be as shown in the table below. 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 clothing 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. W-Mart wants to know the floor space that should be devoted to each department in order to maximize profit. Department Men's clothing Women's clothing Children's clothing Toys Housewares Profit per square feet $4.25 5.10 4.50 5.20 4.10 4.90 Electronics Auto supplies 3.80
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer
c. 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 W-Mart’s decision in (a)?
Transcribed Image Text:W-Mart
W-Mart, a discount store chain, is to build a new store in Alabama. 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, W-Mart estimates its annual profit per square foot for each of the store's
departments to be as shown in the table below.
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 clothing 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. W-Mart wants to know the floor space that should be devoted to each
department in order to maximize profit.
Profit per square feet
$4.25
5.10
Department
Men's clothing
Women's clothing
Children's clothing
Toys
Housewares
Electronics
4.50
5.20
4.10
4.90
Auto supplies
3.80
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 6 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
