Tindall Bookstores is a major national retail chain with stores located principally in shopping malls. For many years, the company has published a Christmas catalog that was sent to current customers on file. This strategy generated additional mail order business, while also attracting customers to the stores. However, the cost effectiveness of this strategy was never determined. In 2008, John Harris, vice president of markeing, conducted a major study on the effectiveness of direct- mail delivery of Tindall’s Christmas catalog. The results were favorable: Patrons who were catalog recipients spent more, on average, than did comparable nonrecipients. These revenue gains more than compensated for the costs of production, handling, and mailing, which had been substantially reduced by cooperative allowances from suppliers. With the continuing interest in direct mail as a vehicle for delivering holiday catalogs, Harris continued to investigate how new customers could most effectively be reached. One of these ideas involved purchasing mailing lists of magazine subscribers through a list broker. To determine which magazines might be more appropriate, a mail questionnaire was administered to a sample of current customers to ascertain which magazines they regularly read. Ten magazines were selected for the survey. The assumption behind this strategy is that subscribers of magazines that a high proportion of current customers read would be viable targets for future purchases at Tindall stores. The question is which magazine lists should be purchased to maximize reaching of potential customers in the presence of a limited budget for purchasing lists. Data from the customer survey have begun to trickle in. The information about the 10 magazines to which a customer subscribes is provided on the returned questionnaire. Harris has asked you to develop a prototype model, which later can be used to decide which lists to purchase. So far only 53 surveys have been returned. To keep the prototype model manageable, Harris has instructed you to go ahead with the model development using the data from the 53 returned surveys. These data are shown in Table 15.4. The costs of the first 10 lists are given next, and your budget is $ 3,000.
a. What magazines should be chosen to maximize overall exposure?
b. Conduct a budget sensitivity analysis on the Tindall magazine list– selection problem. Solve the problem for a variety of budgets and graph percentage of total reach ( number reached/ 53) versus budget amount. As an analyst, make a recommendation as to when an increment in budget is no longer warranted.

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Magazines Customer Customer Magazines 1 10 20 4, 7 1, 4 29 6 3 1 30 3, 4, 5, 10 4 5, 6 31 4 5 32 6 10 33 1, 3, 10 7 2,9 34 4, 5 8 5, 8 35 1,5, 6 9 1, 5, 10 36 1, 3 10 4, 6, 8, 10 37 3, 5, 8 11 38 12 3 39 2, 7 13 40 2, 7 14 41 7 15 42 4, 5, 6 16 6 43 None 17 4, 5 44 5, 10 18 7 45 1, 2 19 5, 6 46 7 50 2, 8 47 1, 5, 10 21 7,9 48 3 22 6 49 1, 3, 4 23 3, 6, 10 50 None 24 None 51 2,6 25 5. 8 52 None 26 3, 10 53 2, 5, 0, 9, 10 27 2, 8