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. Applecore Children€™s Clothing is a retailer that sells high-end clothes for toddlers (ages
1€“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 1200 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 of 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 ten news sites in the questionnaire. The costs of ads per week for the ten Web sites are given in the following table, and the budget is $10,000 per week. For each of the 53 responses received, which of the ten Web sites are regularly visited is given as 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.
Data for Applecore Customer Visits to News Web sites (respondents 5€“33 hidden).

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Website 1 2 345 678 9 10 Cost/Wk ($000) $5.0 $8.0 $3.5 $5.5 $7.0 $4.5 $6.0 $5.0 $3.0 $2.2 Website Customer 2 3 4 5 67 8 9 10 34 35 36 37 38 39 40 41 42 43 0 0 0 01 45 46 47 48 49 50 0 53