Q&H Company advertises during soap operas and football games. Each soap opera ad costs $50,000, and each football game ad costs $100,000. If S soap opera ads are purchased, they will be seen by 5S 1/2...

Q&H Company advertises during soap operas and football games. Each soap opera ad costs $50,000, and each football game ad costs $100,000. If S soap opera ads are purchased, they will be seen by 5S^1/2
million men and 20S^1/2
million women. If F football ads are purchased, they will be seen by 17F^1/2
million men and 7F^1/2
million women. The company wants at least 40 million men and at least 60 million women to see its ads.


a.  Determine how to minimize Q&H’s cost of reaching the required number of viewers.


b.  How does this model violate the proportionality and additivity assumptions of LP?

c.  Suppose that the number of women (in millions) reached by F football ads and S soap opera ads is 7F^1/2
+ 20S^1/2
- 0.2(FS)
^1/2
. Why might this be a more realistic representation of the number of women viewers seeing Q&H’s ads?