Need help with a word problem.

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KOAS

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Apr 26, 2013
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Alright so I'm studying for a final in College Algebra that I will be taking next week. My teacher gives some example problems before each major test so we can get some good practice in.. well I'm having some difficulties with this one. By the way I hope this is the right place to ask this question. If not I' m sorry..
I have no idea how to set up the equation to this so any help is much appreciated!

The directions are:

Solve each problem using quadratic functions.

The question is as follows:

A movie rental company has 1000 subscribers, and each pays $15 per month. On the basis of a survey, company managers feel that for each decrease of $0.25 on the monthly rate, they could obtain 20 additional subscribers. At what rate will maximum revenue be obtained and how many subscribers will it take at that rate?
 
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My plan of attack here would be to use the point-slope formula to determine the linear relationship between the number of subscribers and the monthly rate. Can you identify the given point and slope?

Next, I would use the fact that revenue is the product of the number of subscribers and the monthly rate, and this will give you a quadratic in the monthly rate, for which you can then determine the axis of symmetry, which will tell you the rate which optimizes the revenue. Then, to find the number of subscribers there are at this rate, plug the rate your found which optimizes revenue into the linear relation between subscribers and monthly rate you found earlier.
 
You may be right, in this part of the world, College Algebra is a course taken prior to calculus. I will go to the corner instead for making an assumption...:D
 
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