Case Problem 1: Planning an Advertising Campaign
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 new customers
The Linear Programming Model and solution are as follows:
MAX 90T1+55T2+25R1+20R2+10N1+5N2
S.T.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
1T1<=10
1R1<=15
1N1<=20
10000T1+10000T2+3000R1+3000R2+1000N1+1000N2<=279000
4000T1+1500T2+2000R1+1200R2+1000N1+800N2>=100000
-2T1-2T2+1R1+1R2>=0
1T1+1T2<=20
10000T1+10000T2>=140000
3000R1+3000R2<=99000
1000N1+1000N2>=30000
OPTIMAL SOLUTION
Optimal Objective Value
2160.00000
Variable
Value
Reduced Cost
T1
10.00000
0.00000
T2
5.00000
0.00000
R1
15.00000
0.00000
R2
18.00000
0.00000
N1
20.00000
0.00000
N2
10.00000
0.00000
Constraint
Slack/Surplus
Dual Value
1
0.00000
35.00000
2
0.00000
5.00000
3
0.00000
5.00000
1.
4
0.00000
0.00550
5
27100.00000
0.00000
6
3.00000
0.00000
7
5.00000
0.00000
8
10000.00000
0.00000
9
0.00000
0.00117
10
0.00000
-0.00050
Objective
Allowable
Allowable
Coefficient
Increase
Decrease
90.00000
Infinite
35.00000
55.00000
11.66667
5.00000
25.00000
Infinite
5.00000
20.00000
5.00000
3.50000
10.00000
Infinite
5.00000
5.00000
0.50000
Infinite
RHS
Allowable
Allowable
Value
Increase
Decrease
10.00000
5.00000
10.00000
15.00000
18.00000
15.00000
20.00000
10.00000
20.00000
279000.00000
15000.00000
10000.00000
100000.00000
27100.00000
Infinite
0.00000
3.00000
Infinite
20.00000
Infinite
5.00000
140000.00000
10000.00000
Infinite
99000.00000
10000.00000
5625.00000
30000.00000
10000.00000
10000.00000
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
Television
Radio
Newspaper
Totals
Number of Ads
15
33
30
78
Total Exposure Rating:
Total New Customers Reached:
2.
Budget
$150,000
99,000
30,000
$279,000
2,160
127,100 (Surplus constraint 5)
The dual value shows that total exposure increases 0.0055 points for each one dollar increase in the
advertising budget. Right Hand Side Ranges show this dual value applies for a budget increase of up
to $15,000. Thus the dual value applies for the $10,000 increase.
Total Exposure Rating would increase by 10,000(0.0055) = 55 points
A $10,000 increase in the advertising budget is a 3.6% increase. But, it only provides a 2.54%
increase in total exposure. Management may decide that the additional exposure is not worth the
cost. This is a discussion point.
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.
Remove constraint #5 for the linear programming model and use it to develop the objective function:
MAX 4000T1+1500T2+2000R1+1200R2+1000N1+800N2
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
Television
Radio
Newspaper
Totals
Number of Ads
14
28
55
97
Total New Customers Reached:
Budget
$140,000
83,000
55,000
$279,000
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 number of potential new customers reached looks
attractive. The total number of ads is increased from 78 to 97 (24%) and the number of potential
new customers reached is increased by 139,600 – 127,100 = 12,500 (9.8%).
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 (1.4%).
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. Basically, there
are two good media allocation solutions for this problem.