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Chapter 13: Integer Linear Optimization Models Case Problem: Applecore Children’s Clothing
Book Title: Business Analytics
Printed By: Jigar Jitendrak Patel ([email protected])
© 2021 Cengage Learning, Cengage Learning
Chapter Review
Case Problem: Applecore Children’s Clothing
Applecore Children’s Clothing is a retailer that sells high-end clothes for toddlers (ages 1 to
3), primarily in shopping malls. Applecore also has a successful Internet-based sales
division. Recently Dave Walker, vice-president of the e-commerce division, has been given
the directive to expand the company’s Internet sales. He commissioned a major study on
the effectiveness of Internet ads placed on news web sites. The results were favorable:
Current patrons who purchased via the Internet and saw the ads on news web sites spent
more, on average, than did comparable Internet customers who did not see the ads.
With this new information on Internet ads, Walker continued to investigate how new Internet
customers could most effectively be reached. One of these ideas involved strategically
purchasing ads on news web sites prior to and during the holiday season. To determine
which news sites might be the most effective for ads, Walker conducted a follow-up study.
An e-mail questionnaire was administered to a sample of 1,200 current Internet customers
to ascertain which of 30 news sites they regularly visit. The idea is that web sites with high
proportions of current customer visits would be viable sources of future customers for
Applecore products.
Walker would like to ascertain which news sites should be selected for ads. The problem is
complicated because Walker does not want to count multiple exposures. So, if a respondent
visits multiple sites with Applecore ads or visits a given site multiple times, that respondent
should be counted as reached but not more than once. In other words, a customer is
considered reached if he or she has visited at least one web site with an Applecore ad.
Data from the customer e-mail survey have begun to trickle in. Walker wants to develop a
prototype model based on the current survey results. So far, 53 surveys have been
returned. To keep the prototype model manageable, Walker wants to proceed with model
development using the data from the 53 returned surveys and using only the first 10 news
sites in the questionnaire. The costs of ads per week for the 10 web sites are given in the
following table, and the budget is $10,000 per week. For each of the 53 responses received,
the 10 web sites visited regularly are shown below. For a given customer–web site pair, a
one indicates that the customer regularly visits that web site and a zero indicates that the
customer does not regularly visit that site.
Managerial Report
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1. Develop a model that will allow Applecore to maximize the number of
customers reached for a budget of $10,000 for one week of promotion.
2. Solve the model. What is the maximum number of customers reached for the
$10,000 budget?
3. Perform a sensitivity analysis on the budget for values from $5,000 to $35,000
in increments of $5,000. Construct a graph of percentage reach versus
budget. Is the additional increase in percentage reach monotonically
decreasing as the budget allocation increases? Why or why not? What is your
recommended budget? Explain.
Data for Applecore Customer Visits to News Web Sites
(respondents 5 to 33 hidden)
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Chapter 13: Integer Linear Optimization Models Case Problem: Applecore Children’s Clothing
Book Title: Business Analytics
Printed By: Jigar Jitendrak Patel ([email protected])
© 2021 Cengage Learning, Cengage Learning
© 2022 Cengage Learning Inc. All rights reserved. No part of this work may by reproduced or used in any form or by any means –
graphic, electronic, or mechanical, or in any other manner – without the written permission of the copyright holder.
