American Dream, is a retail and entertainment complex located in the Meadowlands Sports Complex in Rutherford, NJ. The mega-sized mall opened only a few months prior to the start of COVID in the United States. Given their untimely launch and negative press, they have been working hard to promote their 3-million square foot retail and entertainment establishment. The management team requested your recommendations on how to allocate their digital advertising budget across Social Media, Satellite Radio (such as SiriusXM), and Music Streaming Services (such as Spotify). American Dreams digital marketing budget for next quarter is set at $375,000.

The marketing agency has provided the following information about the industry exposure effectiveness rating per ad, the estimate of the number of potential new customers reached per ad, and the cost for each ad.

MEDIA	Effectiveness Metric per Ad	New customers per Ad	Cost per Ad
Social Media	100	4000	$9,000
Satellite Radio	30	2000	$3,000
Music Streaming Services	15	1000	$1,000

The effectiveness metric scores the value of the ad to existing customers and potential new customers. The score is based on qualitative measures such as image satisfaction, message recall, and visual and audio appeal. More expensive Social Media ads will have higher effectiveness scores along with greater potential for reaching new customers.

While the effectiveness metric is a great means to compare campaigns, the score itself is only applicable to the first few advertisements in each medium. For example, Social Media has an effectiveness metric of 100 and a reach to 4000 new customers per ad. These scores are only reliable for the first 14 Social Media ads. After 14 ads, the benefit declines. For purposes of analysis, you can assume that the effectiveness metric for Social Media drops to 65 and the potential new customers reached drops to 1500 per Social Media ad beyond the first 14. For Satellite Radio ads, the effectiveness metric is only reliable for a maximum of 20 ads. After the 20 ads, the effectiveness metric declines to 20 and the number of new customers reached declines to 1200 per ad. Similarly, for Music Streaming Services ads, the effectiveness metric is only reliable for a maximum of 27 ads; the effectiveness metric declines to 8 and the potential number of new customers reached declines to 200 per ad.

American Dreams management team accepted maximizing the total effectiveness metric, across all media, as the objective of this digital advertising campaign; however, they are insisting that the total of all ads purchased must reach at least 100,000 new customers. American Dreams management team also insist on the following guidelines:

Use at least twice as many Satellite Radio ads as Social Media ads

Use no more than 20 Social Media advertisements.

The Social Media budget should be at least $160,000

The Satellite Radio budget is restricted to a maximum of $150,000

The Music Streaming Services budget is to be at least $35,000

Use optimization techniques to provide a recommendation on how to best allocate the $375,000 advertising budget across these three digital marketing options. Develop a linear programming model that can be used to optimize the advertising budget allocation. (HINT: you should define two variables for each media option (eg. S1 = number of Social Media advertisements with rating of 100 and 4000 new customers and S2 = number of Social Media advertisements with rating of 65 and 1500 new customers, and so on). Enter the problem into Excel and use Solver to solve for the optimal solution.