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:

 

Maximize 90T1+55T2+25R1+20R2+10N1+5N2

 

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

       6)  -2T1-2T2+1R1+1R2>=0

       7)  1T1+1T2<=20        8)  10000T1+10000T2>=140000

       9)  3000R1+3000R2<=99000       10)  1000N1+1000N2>=30000

 

Solutions:

 

 

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

 

Advertising Schedule:

 

Media

No. of Ads

Budget

Television

15

$150,000

Radio

33

99,000

Newspaper

30

30,000

Totals

78

$279,000

 

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

 

           Advertising Schedule:

 

Media

No. of Ads

Budget

Television

14

$140,000

Radio

28

83,000

Newspaper

55

55,000

Totals

97

$279,000

 

           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.