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Linear Programming Case Study

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Linear Programming

INFO562-64

Dr. Nicole Koppel and Professor Teresa Dantzler

By: Vincent Nicastro and Rhonda Sharif

  1. Case Synopsis

Street Vibes is a Miami, Florida-based upscale dance club that has hired the advertising firm of Mayer, Mann, and Merlin (MMM) to help its management formulate a marketing plan for the coming season. Street Vibes management has sought MMM’s recommendation concerning how the management team should distribute the advertising budget across the three advertising channels the company uses namely: SiriusXM, Social Media, and Internet Radio. Additionally, Street Vibes management wants MMM consultants to determine the impact a $25,000 reduction in budgeted advertising funds would have on the marketing plan. The company’s budget for the coming season is $375,000, but the three advertising channels differ in terms of exposure rating, new customers reached and cost, thus Street Vibes management wants MMM consultant’s help in determining the optimal marketing decisions.

  1. Methodology

                MMM consultants used linear programming based on the information provided by the management of Street Vibes. The management provided vital information such as the projected exposure rating per ad, new customers per ad and cost per ad from which MMM consultants were able to determine the reliability of the exposure ratings based on the number of ads for each media. The following is the mathematical programming model based on the data provided by management of Street Vibes:

S1- number of SiriusXM advertisements with rating of 100 and 4000 new customers

S2 - number of SiriusXM advertisements with rating of 65 and 1500 new customers

S3- number of Social Media advertisements with rating of 30 and 2000 new customers

S4- number of Social Media advertisements with rating of 20 and 1200 new customers

S5- number of Internet Radio advertisements with rating of 15 and 1000 new customers

S6- number of Internet Radio advertisements with rating of 8 and 200 new customers

N1: no. of ads for SiriusXM

N2: no. of ads for Social Media

N3: no. of ads for Internet Radio

Constraints:

N1*(S1+S2)≥160000

N2*(S3+S4)≤150000

N3*(S5+S6)≥35000

N1≤20

N2≥2*N1

  1. Findings and Conclusions

Street Vibe’s optimal marketing decision would be to allocate $171,000 for SiriusXM ads, $150,000 for Social Media ads and $54,000 to Internet Radio ads. This mix of advertising would enable Street Vibe to reach a total of 171,900 new customers with Social Media being the most effective channel with a total of 76,000 new customers reached. However, if the budget is reduced by $25,000, then Street Vibe should set aside $162,000 for SiriusXM ads and $38,000 for Internet Radio ads. The budget for Social Media ads should remain unchanged. The following tables present a summary schedule showing the recommended number of SiriusXM, Social Media, and Internet Radio advertisements and the budget allocation for each medium:

 

Variables

Number of Ads

Exposure Rating per Ad

New Customer per Ad

Total Customers Reached

Cost per Ad

Budget

SiriusXM

S1

14

100

4000

56000

9000

 

 

S2

5

65

1500

7500

 

$171,000

 

 

19

 

 

 

 

 

 

 

 

 

 

 

 

 

Social Media

S3

20

30

2000

40000

3000

 

 

S4

30

20

1200

36000

 

 

 

 

50

 

 

 

 

$150,000

 

 

 

 

 

 

 

 

Internet Radio

S5

27

15

1000

27000

1,000

 

 

S6

27

8

200

5400

 

 

 

 

54

238

 

171900

 

$54,000

Table 1: Advertising budget of $375,000

 

Variables

Number of Ads

Exposure Rating per Ad

New Customer per Ad

Total Customers Reached

Cost per Ad

Budget

SiriusXM

S1

14

100

4000

56000

9000

 

 

S2

4

65

1500

6000

 

$162,000

 

 

18

 

 

 

 

 

 

 

 

 

 

 

 

 

Social Media

S3

20

30

2000

40000

3000

 

 

S4

30

20

1200

36000

 

 

 

 

50

 

 

 

 

$150,000

 

 

 

 

 

 

 

 

Internet Radio

S5

27

15

1000

27000

1,000

 

 

S6

11

8

200

2200

 

 

 

 

38

238

 

167200

 

$38,000

         

...

...

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