Problem 3: Application of Linear Programming in Marketing: Media Selection Probl
ID: 355815 • Letter: P
Question
Problem 3: Application of Linear Programming in Marketing: Media Selection Problem We-Ad Agency was hired by a presidential candidate campaign to prepare an ad targeting a specific class of audience in the State of New York during the 2016 election. The "target audience" had the following characteristics with relative importance of each mentioned in (): 1) Sex: Male (0.25) 2) Age: 40+ (0.15) 3) Education: High School Graduate (0.25) 4) Family Income: below $60k (0.35) The maximum allowable budget to this ad was set at $750,000 per week by the campaign manager. We-Ad agency made a careful analysis of the 3 available media (social media, radio and television), and came up with the data in the table below. The percentages are the expected proportion of the audience within each characteristic group (sex, age, etc.) using these three types of media on a frequent basis. Social d Radio Television Media 40% 35% Sex: Male Age: 40+ Education: High School Graduate | 4090 Income: below $60k Audience Size2,800,000 1,800,000 2,200,000 60% 50% | 60% 70% 80% 75% | 90% 80% | 30% Furthermore, the cost and the maximum allowed number of ads in each medium are shown in the table below: Social Radio Television Cost/Ad Max # of ads allowed $7,500 9,000 $15,000 25 30 30 The objective here is to maximize the total effective exposure for all the advertising employed Assume you were asked to utilize your linear programming skills to help the Agency with this important matter Problem 3 continued on the next page)Explanation / Answer
Ans a.
x : No of Social Media ads
y: No of radio ads
z: No of TV ads
Audience size as per the expected percentage proportion provided in the problem
Social Media
Radio
TV
Sex: Male
40%
60%
80%
Age = 40+
35%
50%
75%
Education
40%
60%
90%
Income Bellow 60K
30%
70%
80%
Audience Size
2800000
1800000
2200000
Social Media
Radio
TV
Sex: Male
1120000
1080000
1760000
Age = 40+
980000
900000
1650000
Education
1120000
1080000
1980000
Income Bellow 60K
840000
1260000
1760000
Audience Size
2800000
1800000
2200000
Calculating effectiveness of an ad using relative importance of each characteristics :
Social Media = 1120000 * 0.35 + 980000 * 0.15 + 1120000 * 0.25 + 840000 * 0.35 = 1113000
Radio = 1080000 * 0.35 + 900000 * 0.15 + 1080000 * 0.25 + 1260000 * 0.35 = 1224000
TV = 1760000 * 0.35 + 1650000 * 0.15 + 1980000 * 0.25 + 1760000 * 0.35 = 1974500
Ans b . So Objective Function is to maximize the total effectiveness
N = 111300x + 1224000y + 1974500z
Anc c. Constraints:
Maximum Budget is 750000
As per the cost/ad given the problem
7500x + 9000y + 15000z <= 750000
Ans d . Maximum Media ads as per the problem:
x <=25
y <=30
z <=30
Social Media
Radio
TV
Sex: Male
40%
60%
80%
Age = 40+
35%
50%
75%
Education
40%
60%
90%
Income Bellow 60K
30%
70%
80%
Audience Size
2800000
1800000
2200000
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