The decision variables are as follows:
T1 = No. of tv advertisements with rating of 90 and 4000 new customers
T2 = No. of tv advertisements with rating of 40 and 1500 new customers
R1 = No. of radio advertisements with rating of 25 and 2000 new customers
R2 = No. of radio advertisements with rating of 15 and 1200 new customers
N1 = No. of newspaper advertisements with rating of 10 and 1000 new customers
N2 = No. of newspaper advertisements with rating of 5 and 800 new customers
The Linear Programming Model and solution are as follows:
Subject to constraints
1) 1T1<=10 2) 1R1<=15 3) 1N1<=20 4) 10000T1+10000T2+3000R1+3000R2+1000N1+1000N2<=279000 5) 4000T1+1500T2+2000R1+1200R2+1000N1+800N2>=100000
7) 1T1+1T2<=20 8) 10000T1+10000T2>=140000
9) 3000R1+3000R2<=99000 10) 1000N1+1000N2>=30000
1. Summary of the Optimal Solution
T1 + T2 = 10 + 5 = 15 Television advertisements
R1 + R2 = 15 + 18 = 33 Radio advertisements
N1 + N2 = 20 + 10 = 30 Newspaper advertisements
No. of Ads
Total Exposure Rating: 2,160
Total New Customers Reached: 127,100
2. By $10,000 increase in the advertising budget, it only provides a increase in total exposure to 2215 from 2160. Management may decide that the additional exposure is not worth the cost.
3. The ranges for the exposure rating of 90 for the first 10 television ads show that the solution remains optimal as long as the exposure rating is 55 or higher. This indicates that the solution is not very sensitive to the exposure rating HJ has provided. Indeed, we would draw the same conclusion after reviewing the next four ranges. We could conclude that Flamingo does not have to be concerned about the exact exposure rating. The only concern might be the newspaper exposure rating of 5. A rating of 5.5 or better can be expected to alter the current optimal solution.
4. Develop the new objective function:
Maximise 4000T1+1500T2+2000R1+1200R2+1000N1+800N2 (No of Customers)
Solving provides the following Optimal Solution
T1 + T2 = 10 + 4 = 14 Television advertisements
R1 + R2 = 15 + 13 = 28 Radio advertisements
N1 + N2 = 20 + 35 = 55 Newspaper advertisements
No. of Ads
Total New Customers Reached 139,600
Total Exposure Rating
90(10) + 55(4) + 25(15) + 20(13) + 10(20) + 5(35) = 2130
5. The solution with the objective to maximize the No. of potential new customers reached looks attractive. The total No. of ads is increased from 78 to 97 and the No. of potential new customers reached is increased by 139,600 – 127,100 = 12,500.
Maximizing total exposure may seem to be the preferred objective because it is a more general measure of advertising effectiveness. Exposure includes issues of image, message recall and appeal to repeat customers. However, in this case, many more potential new customers will be reached with the objective of maximizing reach, and the total exposure is only reduced by 2160 – 2130 = 30 points.
At this point, we would expect some discussion concerning which solution is preferred: the one obtained by maximizing total exposure or the one obtained by maximizing potential new customers reached. Expect students to have differing opinions on the final recommendation. There are two good media allocation solutions for this problem.