Question

Hampton Commission on the Arts (HCA) is planning on advertising its upcoming events. A local newspaper claims that the ads on the paper can reach 27,000 art lovers, and it costs the HCA $6,000. Advertising on a local radio $10,000, and it is estimated to reach an audience of 39,000 people. HCA also considers google ads, which costs $15,000 will supposedly reach 52,000 arts customers. The breakdown of the audience for each type of commercial is as follows (charts below):

HCA has determined some marketing guidelines in order to improve outreach efforts. It wants to reach at least 200,000 potential arts customers. Past experience shows that older people are more likely to buy tickets than younger people; the number of potential customers over 35 should be at least 50% more than the potential customers under 35. The council also believes women are more likely to initiate ticket purchases to the arts than men, so it wants its advertising audience to be at most 40% male.

1) Construct a mathematical model for HCA to determine the number of ads of each type it should use at the minimum cost.

2) Solve the model using Excel Solver

Radio Ad				Newspaper Ad				Google Ads
Age	Male	Female		Age	Male	Female		Age	Male	Female
≥ 35	9,000	15,000		≥ 35	7,000	9,000		≥ 35	7,000	8,000
< 35	6,000	9,000		< 35	6,000	5,000		< 35	18,000	19,000

Answer 1

Considering all the constraints, we have developed the mathematical model for the given problem and solved using excel solver. For this problem, there is no feasible integer solution.