Question

Case Problem1 PLANNING AN ADVERTISING CAMPAIGN The Flamingo Grl is an upscale restaurant located in St. Petersburg. Florida. To help plan an advertising campaign for the coming season, Flamingo's management team hired the advertising firm of Haskell & Johnson (HJ). The management team requested HJ's recom- mendation concerning how the advertising budget should be distributed across television radio, and online advertisements. The budget has been set at $279,000. In a meeting with Flamingo's management team, HJ consultants provided the following information about the industry exposure effectiveness rating per ad, their estimate of the number of potential new customers reached per ad, and the cost for each ad New Customers Cost xposure Advertising Media Rating per Ad per Ad per Ad Television 90 4,000 2,000 $10,000 $ 3.000 $ 1,000 Radio 25 Online 10 1,000 The exposure rating is viewed as a measure of the value of the ad to both existing customers and potential new customers. It is a function of such things as image, message recal, visual and audio appeal, and so on. As expected, the more expensive television advertisement has the highest exposure effectiveness rating along with the greatest potential for reaching new customers At this point, the HJ consultants pointed out that the data concerning exposure and reach were only applicable to the first few ads in each medium. For television HJ stated that the exposure rating of 90 and the 4000 new customers reached per ad were reliable for the fist 10 television ads. After 10 ads, the benefit is expected to decline. For plan- ning purposes, HJ recommended reducing the exposure rating to 55 and the estimate of the potential new customers reached to 1500 for any television ads beyond 10. For radio ads, the preceding data are reliable up to a maximum of 15 ads. Beyond 15 ads, the exposure rating declines to 20 and the number of new customers reached declines to 1200 per ad. Similarly, for online ads, the preceding data are reliable up to a maximum of 20; the exposure rating declines to 5 and the potential number of new customers reached declines to 800 for additional ads. Flamingo's management team accepted maximizing the total exposure rating. across all media, as the objective of the advertising campaign. Because of management's concern with attracting new customers, management stated that the advertising campaign must reach at least 100,000 new customers. To balance the advertising campaign and make use of all advertising media, Flamingo's management team also adopted the following guidelines: Use at least twice as Use no more than 20 television -The television budget should be at least $140,000. . The radio advertising budget is restricted to a maximum of $99,000. .The online budget is to be at least $30,000. radio advertisements as television advertisements, HJ agreed to work with these guidelines and provide a recommendation as to how the $279,000 advertising budget should be allocated among television, radio, and online advertising Managerial Report Develop a model that can be used to determine the advertising budget allocation for the Fla- mingo Grll. Include a discussion of the following in your report: . A schedule showing the recommended number of television, radio, and online adver- tisements and the budget allocation for each medium. Show the total exposure and indicate the total number of potential new customers reached. 2. How would the total exposure change if an additional $10,000 were added to the advertising budget? 3. A discussion of the ranges for the objective function coefficients. What do the ranges indicate about how sensitive the recommended solution is to HJ's exposure rating coefficients? management team asked how 4. After reviewing HJ's recommendation, the Flamingo's managen the recommendation would change if the objective of the advertising campaign was to maximize the number of potential new customers reached. Develop the media schedule under this objective. 5. Compare the recommendations from parts 1 and 4. What is your recommendation for the Flamingo Grill's advertising campaign?

Answer 1

Answer:

The decision variables are as follows: T1- number of television advertisements with rating of 90 and 4000 new customers T2- number of television advertisements with rating of 40 and 1500 new customers R1- number of radio advertisements with rating of 25 and 2000 new customers R2 = number of radio advertisements with rating of 15 and 1200 new customers N1- number of newspaper advertisements with rating of 10 and 1000 new customers N2- number of newspaper advertisements with rating of 5 and 800 newcustomers The Linear Programming Model and solution using The Management Scientist follow: MAX = 90T1+55T2+25R1+20R2+10N1+5N2 Subjectto 1) 1T1 10 2) 1R1<15 3) 1N1<20 4) 1000OT1+10000T2+300OR1+300OR2+1000N1+100ON2<279000 5) 4000T1+1500T2+2000R1+1200R2+1000N1+800N2 100000 6) -2T1-2T2+1R1+1R2 0 7) 1T1+1T2<20 8) 10000T1+10000T2 140000 9) 3000R1+3000R2 99000 10) 1000N1+1000N2>30000

PPTIMAL SOLUTION Objective Function Value 2160.000 Objective Function Value 2160.000 Variable Value Reduced Costs T1 10.000 0.000 T2 5.000 0.000 R1 15.000 0.000 R2 18.000 0.000 N1 20.000 0.000 N2 10.000 0.000 Constraint Slack/Surplus Dual Prices 0.000 35.000 0.000 5.000 0.000 5.000 0.000 0.006 27100.000 0.000 3.000 0.000 5.000 0.000 10000.000 0.000 0.000 0.001 10 0.000 0.000

DBJECTIVE COEFFICIENT RANGES ariable Loer Limit Current Value Upper Limit T1 55.000 90.000 No Upper Limit T2 No Lower Limit 55.000 66.667 R1 20.000 25.000 No Upper Limit R2 16.500 20.000 25.000 N1 5.000 10.000 No Upper Limit 5.500 N2 No Lower Limit 5.000 RIGHT HAND SIDE RANGES Constraint Lowe Limi Current Value Upper Limit 0.000 10.000 15.000 0.000 15.000 33.000 0.000 20.000 30.000 269000.000 279000.000 294000.000 5 No Lower Limit 100000.000 127100.000 3.000 6 No Lower Limit 0.000 15.000 20.000 No Upper Limit 8 No Lower Limit 140000.000 150000.000 93375.000 99000.000 109000.000 10 20000.000 30000.000 40000.000

1. Summary of the Optimal Solurtion T1 + T2 =110 + 5 = 15 Television advertisements RiR2 15 18 33 Radio advertisements N1 + N2 = 20 +10 = 30 Newspaper advertisements Advertising Schedule: Media Number of Ads Budget Television 15 Si50,CC0 Radio 33 99,0C0 Newspaper 30 30,000 Totals 78 S279,000 Total Exposure Rating: 2,160 Total New Customers Reached: 127,30o (Surplus constraint 5) 2. The dual price indicates that the total exposure increases by 0.006 points for every dollar increase in the budget of advertising. Right hand side range shows the dual price which is applicable for increase in budget up to $294,000 $279,000 S15,000. Hence, the dual price is applicable for increase in $10,000. Increase in total exposure rating would be i0,000 (0.0C6) 60 points. A S10,C00 increase in advertising budget is equal to increase of 3.6%. It only provides increase of 2.8% in the total exposure.

3. The range for the exposure rating is 90 for the first 10 television ads which show that the solution is optimal till the rating of exposure is above or equal to 55. The solution is insensitive to exposure rating provided by HI. Similar conclusion would be drawn ařter the revision of next four ranges. We can conclude that Flamingo should not be concern about the appropriate exposure rating. The main concern might be the rating of 5. A rating equal to 5.5 or higher can be expected in altering the present optimal solution 4. Remove constraint #5 for the linear programming model and use it to develop the objective function: MAX 40COTi+150OT2+2000R1+12COR 2+1000N1+800N2 Solving provides the following Optimal Solution T1 + T2:10 +4=14 Television advertisements Ri R2 15 13 28 Radio advertisements NI +N2 20 35 55 Newspaper advertisements Advertising Schedule: Media Number of Ads Budget Television 14 $140,000 Radio 28 83,000 Newspaper 55 55,000 Totals 97 $279,000

p. The solution along with the objective maximizes the number of potential nev customers is reached which looks attractive. The total number of ads increased by 24% that is 78 to 97 and the number of potential new customers reached increased by 9.8% equal to $139,600 $127,100 $12,500. Maximizing of total exposure appears to be preferred objective because it is more of general measure. Exposure includes appeal to repeat customers, message recall and issue of image. In this case, more potential new customers which will be reached with maximizing each and total exposure is reduce by only 1.4% equal to 2160-2130-30. As there are two good media of allocating solutions to this problem, so we expect students to have different opinion on the recommendation