(33 points) Formulate the following mathematical program (do not solve). Grabiec
ID: 376447 • Letter: #
Question
(33 points) Formulate the following mathematical program (do not solve). Grabiec Keno Enterprises (GKE) is trying to determine three goals for its advertising campaign: 3) the best advertising schedule. GKE has the following a. Advertisements should be seen by at least 40 million high income men (HM) b. Advertisements should be seen by at least 60 million low income people (LP) c. Advertisements should be seen by at least 35 million high income women (HW) GKE can purchase two types of advertisements: 1) during football games; and 2) during reality shows. At most $600,000 can be spent on advertising. The costs (per minute) and potential audiences are shown below. Football Reality HM 7 million 3 million LP 10 million 5 million HW 5 million 4 million Cost $100,000 $60,000 Assume goal b is twice as important as goal a and goal cExplanation / Answer
Decision variables:
F = Minutes of Football game advts to buy
R = Minutes of Reality show advts to buy
Objective: Min (60/40)*d1- + 2*d2- + (60/35)*d3-
s.t.
100000F + 60000R <= 600000
7F + 3R - d1+ + d1- = 40
10F + 5R - d2+ + d2- = 60
5F + 4R - d3+ + d3- = 35
F, R, d1+, d1-, d2+, d2-, d3+, d3- >= 0
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