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linear program

The SMM Company,which is manufacturing a new instant salad machine, has $350,000 to spend on advertising. The product is only to be test marketed initially in the Dallas area. The money is to be spent on an advertising blitz during one weekend( Friday, Saturday, Sunday) in January and SMM is limited to television advertising.
The company has three options available: day time advertising, everything news advertising and the Super Bowl. Even though the Super Bowl is a national telecast, the Dallas Cowboys will be playing in it and hence, the viewing audience will be epecially large in the Dallas area. A mixture of one minute TV sports is desired. The table below gives pertinent data:

Cost Per Ad Estimated New Audience Reached with Each Ad
Day Time $5000 3000
Evening News $7000 4000
Super Bowl $100,000 75000

SMM has decided to take out at least one ad in each option. Further, there are only two Super Bowl ad spots available. There are 10 day time spots and 6 evening spots available daily. If SMM wants to have at least 5 ads per day, but spend no more than $50,000 on Friday and no more than $75,000 on Saturday, formulate a linear program to help SMM decide how the company should advertise over the weekend.

Solution Preview

OK, first set up the variables. Suppose, we order
x1 Day Time ads on Friday,
x2 Evening Time ads on Friday
x3 Day Time ads on Saturday
x4 Evening Time ads on Saturday
x5 Day Time ads on Sunday
x6 Evening Time ads on Sunday
x7 Super Bowl ads in total

We obviously want to maximize the audience reached. So, let's formulate the ...

Solution Summary

Formulate a linear program to help SMM decide how the company should advertise over the weekend.

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