"Management Science" Give me a RECOMMENDATION for this case study, please, Thank you! no need to answer all the letters problems, just a RECOMMENDATION for this case study only

Case 5-1 Selling Soap Reconsider the Profit & Gambit Co. advertising-mix problem presented in Section 2.7. Recall that a major advertising campaign is being planned that will focus on three key products: a stain remover, a liquid detergent, and a powder detergent Management has made the following policy decisions about what needs to be achieved by this campaign. Sales of the stain remover should increase by at least 3 percent. Sales of the liquid detergent should increase by at least 18 percent Sales of the powder detergent should increase by at least 4 percent. The spreadsheet in Figure 2.21 shows the linear programming model that was formulated for this problem. The minimum required increases in the sales of the three products are given in the data cells Minimum Increase (G8:G10). The changing cells Advertising Units (C14:D14) indicate that an optimal solution for the model is to undertake four units of advertising on television and three units of advertising in the print media. The objective cell TotalCost (G14) shows that the total cost for this advertising campaign would be $10 million. After receiving this information, Profit & Gambit management now wants to analyze the trade-off between the total advertising cost and the resulting benefits achieved by increasing the sales of the three products. Therefore, a management science team (you) has been given the assignment of developing the information that management will need to analyze this trade-off and decide whether it should change any of its policy decisions regarding the required minimum increases in the sales of the three products. In particular, management needs some detailed information about how the total advertising cost would change if it were to change any or all of these policy decisions. a. For each of the three products in turn, use graphical analysis to determine how much the total advertising cost would change if the required minimum increase in the sales of that product were to be increased by 1 percent (without changing the required minimum increases for the other two products). b. Use the spreadsheet shown in Figure 2.21 (available in www.mhhe.com/hillier6e) to obtain the information requested in part a. c. For each of the three products in turn, use a parameter analysis report to determine how the optimal solution for the model and the resulting total advertising cost would change if the required minimum increase in the sales of that product were to be systematically varied over a range of values (without changing the required minimum increases for the other two products). In each case, start the range of values at o percent and increase by 1 percent increments up to double the original minimum required increase. d. Use Solver to generate the sensitivity report and indicate how the report is able to provide the information requested in part d. Also use the report to obtain the allowable range for the required minimum increase in the sales of each product. Interpret how each of these allowable ranges relates to the results obtained in part e. Suppose that all the original numbers in Minimum Increase (G8:G10) were to be increased simultaneously by the same amount. How large can this amount be before the shadow prices provided by the sensitivity report may no longer be valid? f. Below is the beginning of a memorandum from the management science team to Profit & Gambit management that is intended to provide management with the information it needs to perform its trade-off analysis. Write the rest of this memorandum based on a summary of the results obtained in the preceding parts. Present your information in clear, simple terms that use the language of management. Avoid technical terms such as shadow prices, allowable ranges, and so forth. MEMORANDUM To: Profit & Gambit management From: The Management Science Team Subject: The trade-off between advertising expenditures and increased sales As instructed, we have been continuing our analysis of the plans for the major new advertising campaign that will focus on our spray prewash stain remover, our liquid formulation laundry detergent, and our powder laundry detergent. Our recent report presented our preliminary conclusions on how much advertising to do in the different media to meet the sales goals at a minimum total cost: Allocate $4 million to advertising on television Allocate $6 million to advertising in the print media. Total advertising cost: $10 million. Page 198 We estimate that the resulting increases in sales will be Stain remover: 3 percent increase in sales Liquid detergent: 18 percent increase in sales Powder detergent: 8 percent increase in sales You had specified that these increases should be at least 3 percent, 18 percent, and 4 percent, respectively, so we have met the minimum levels for the first two products and substantially exceeded it for the third. However, you also indicated that your decisions on these minimum required increases in sales (3 percent, 18 percent, and 4 percent) had been tentative ones. Now that we have more specific information on what the advertising costs and the resulting increases in sales will be, you plan to reevaluate these decisions to see if small changes might improve the trade-off between advertising cost and increased sales