An advertising campaign for a new breakfast bar will be conducted in Baltimore a

Question

An advertising campaign for a new breakfast bar will be conducted in Baltimore area and may use TV commercials, radio commercials, and newspaper commercials. Information about the three media (for each commercial) is shown below.

Medium Cost Consumers Reached Exposure Quality
TV $2500 100000 30
Radio $ 750 25000 40
Newspaper $1500 50000 25

If the number of TV commercials cannot exceed the number of radio commercials by more than 4, and if the advertising budget is $50000, develop the model that will maximize the total number of consumers reached and achieve an exposure quality of at least 500.
Formulate a linear programming model for this problem by defining the decision variables, objective function, and all the constraints. Do NOT solve the problem after formulating.

Explanation / Answer

Decision variables are: 1. Number of TV Commercials (Say x) 2. Number of Radio Commercials (Say y) 3. Number of Newspaper Commercials (Say z) Equation 1 - Total budget = $50000 which gives 2500x + 750y + 1500z = 50000 Equation 2 - Number of TV Commercials cannot exceed Radio commercials by 4 which gives x - y < 4 Equation 3 - Total Exposure quality must be atleast 500 which gives 30x + 40y + 25z = 500 Objective function = Function that needs to be maximized = Exposure quality equation i.e. Equation 3 is the Objective function Constraints are Equations 1 & 2. Hope thats clear.

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