Linear programming model to get the optimal schedule of tv

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Reference no: EM132187078

The General Flakes Company sells a brand of low-fat breakfast cereal that appeals to people of all age groups and both genders. The company advertises this cereal in a variety of 30-second TV ads, and these ads can be placed in a variety of TV shows. The ads in different shows vary by cost -some 30-second slots are much more expensive than others- and by the types of viewers they are likely to reach. The company has segmented the potential viewers into six mutually exclusive categories: males age 18 to 35, males age 36 to 55, males over 55, females age 18 to 35, females age 36 to 55, and females over 55. A rating service can supply data on the number of viewers in each of these categories who will watch a 30-second ad on any particular TV show. Each such viewer is called an exposure. The company has determined the required number of exposures it wants to obtain for each group. It wants to know how many ads to place on each of several TV shows to obtain these required exposures at minimum cost. The data on costs per ad, numbers of exposures per ad, and minimal required exposures are listed in the file AdProblem-Template.xls, where number and exposures are expressed in millions, and costs are in thousands of dollars

a) Formulate a linear programming model to get the optimal schedule of TV ads. Provide a math formulation. Keep the variables of the continuous type. The file AdProblem-Template.xlsx provides a template for the LP formulation. Include the Answer Report and the Sensitivity Report as part of your answer.

b) Answer the following questions based on the Sensitivity Report:

i) If the cost of the ad on Sports Center were $9.5K, would the number of ads placed there change? If it were $8.5K instead? Explain.

ii) How much would the company save if the company relaxed the constraint for men in the 36-55 age range to be 55M instead of 60M?

iii) Would the company reduce the cost of the campaign if the requirement of exposures for men in the 18-35 range were 55M instead of 60M?

iv) There is a proposal for an alternative campaign to target females in the age range 18-35 that will provide an exposure of 8 million at cost $65K. Would it make sense to reallocate $65K from the budget for this project and place it on the alternative campaign? Explain.

v) So far, the company is not advertising in CNN. How much should the maximum ad cost in CNN be to become attractive? Explain.

Reference no: EM132187078

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