An apparel company has a successful online sales division. To grow the companys online sales, a major study on the effectiveness of ads placed on news websites was performed. To determine which news sites might be the most effective for ads, the company conducted a follow-up study. A questionnaire was administered to a sample of 1200 current online customers to determine which of 30 news sites they regularly visit. The company wants to determine which news sites should be selected for ads. The company wants to develop an integer optimization model based on the current survey results. The problem is complicated because the company does not want to count multiple exposures. So, if a respondent visits multiple sites with the company 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 website with the company ad. The company wants to develop an integer optimization model based on the current survey results. So far, 53 surveys have been returned. To keep the prototype model manageable, the company 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 websites are given in the following Table 1, and the budget is $10,000 per week. For each of the 53 responses received, which of the ten websites are regularly visited is given in Table 2. apparel ads xls. For a given customerwebsite pair, a one indicates that the customer regularly visits that website, and a zero indicates that the customer does not regularly visit that site. For instance, customer 1 regularly visits only website 10.

Table 1. Weekly cost of putting an ad on each website

Website	1	2	3	4	5	6	7	8	9	10
Cost/Week ($000)	$5.0	$8.0	$3.5	$5.5	$7.0	$4.5	$6.0	$5.0	$3.0	$2.2

a).Develop a binary integer optimization model that will allow the company to maximize the number of customers reached for a budget of $10,000 for one week of promotion (write down decision variables, objective function, constraints).

b).Implement the optimization model in excel and solve the model using solver (copy and paste the results from Excel). What is the maximum number of customers reached for the $10,000 budget?

c). Perform a sensitivity analysis on the budget for values from $5,000 to $35,000 in increments of$5,000. Construct a line chart of percentage reach versus budget. Does the percentage reach increase proportionately as the budget increases? Why or why not? What is your recommended budget? Explain.

Table 2. Apparel ads xls

Clothing Ads data Website Cost/Week (5000) 1 $5.0 2 $8.0 3 $3.5 4 $5.5 5 $7.0 6 $4.5 9 $3.0 10 $2.2 $6.0 Budget (5000) $10.0 $5.0 Website Customer number 2 0 0 3 0 0 4 0 1 ol 0 0 0 0 1 0 0 0 1 0 0 Clothing Ads data Website Cost/Week (5000) 1 $5.0 2 $8.0 3 $3.5 4 $5.5 5 $7.0 6 $4.5 9 $3.0 10 $2.2 $6.0 Budget (5000) $10.0 $5.0 Website Customer number 2 0 0 3 0 0 4 0 1 ol 0 0 0 0 1 0 0 0 1 0 0