Advanced Decision Science Flamingo Grill - Linear Programming Case
Jojo P. Javier October 24, 2015
Introduction The Flamingo Grill’s management team hired the advertising firm Haskell & Johnson to recommend the
optimal advertising mix of television, radio and newspaper ads given a budget of $279,000.00. The following information was provided by H&J:
Advertising Medium TV1 TV2 RD1 RD2 NP1 NP2
Television Radio Newspaper
1ST 10 > 10
Media Exposure Rating 90 55
New Customers per Ad 4,000 1,500
1ST 15 >15 1ST 20 >20
25 20 10 5
2,000 1,200 1,000 800
No of Ads
Cost per Ad $ 10,000 10,000 3,000 3,000 1,000 1,000
The objective of the advertising campaign is to maximize the total exposure rating across all media. Z = 90TV1 + 55TV2 + 25RD1 + 20RD2 +10NP1 + 5NP2 Constraints:
TV budget Radio budget Newspaper budget TV Ads Radio and TV 1ST 10 TV Ads 1ST 15 Radio Ads 1ST 20 News Ads Total budget
Exposure
Non-negativity
10,000TV1 + 10,000TV2 3,000RD1 + 3,000RD2 1,000NP1 + 1,000NP2 TV1 + TV2 RD1 + RD2 – 2TV1 – 2TV2 TV1 RD1 NP1 10,000TV1 + 10,000TV2 + 3,000RD1 + 3,000RD2+ 1,000NP1 + 1,000NP2 4,000TV1 + 1,500TV2 + 2,000RD1 + 1,200RD2 + 1,000NP1 + 800NP2 TV1, TV2, RD1, RD2, NP1, NP2
≥ ≤ ≥ ≤ ≥ ≤ ≤ ≤
140,000 99,000 30,000 20 0 10 15 20
≤
279,000
≥
100,000
≥
0
1. A schedule showing the recommended number of television, radio, and newspaper advertisements and the budget allocation for each media. Show the total exposure and indicate the total number of potential new customers reached.
Medium
Total Ads
T.V.
15
Radio
33
Newspaper
30 Total
No of Ads
New Customers
Exposure
10 5 15 18 20 10 78
40,000 7,500 30,000 21,600 20,000 8,000 127,100
900 275 375 360 200 50 2,160
Budget $100,000 50,000 45,000 54,000 20,000 10,000 $279,000
2. How would the total exposure change if an additional $10,000 were added to the advertising budget? The exposure rating would increase to 2,215 fro m 2,160. Based on the LP solution, only one TV ad will be added given the additional $ 10,000.
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?
The degree of sensitivity for the maximum exposure coeffic ient is low because it is a non-binding (constraint 10 =0). Furthermore, the shadow price of the radio and newspaper ads are in small multiples (.0012 and -.0005) to even make a significant impact on the maximum exposure.
4. After reviewing HJ's recommendation, the Flamingo's management team asked how 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. Change Z to 4,000TV1 + 1,500TV2 + 2,000RD1 + 1,200RD2 + 1,000NP1 + 800NP2
Medium
Total Ads
T.V.
14
Radio
28
Newspaper
55 Total
No of Ads
New Customers
Exposure
10 4 15 13 20 35 97
40,000 6,000 30,000 15,600 20,000 28,000 139,600
900 220 375 260 200 175 2,130
Budget $100,000 40,000 45,000 39,000 20,000 35,000 $279,000
5. Compare the recommendations from parts 1 and 4. What is your recommendation for the Flamingo Grill's advertising campaign? Maximizing the number of new customers is the best option because the potential new customers will increase from 127,100 to 139,6 00. That is a total of 12,500 new customers. This is despite a drop in exposure rating to 2,130.
