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Q&A #323


Factoring and quadratics

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From: Mary Lou (for Teacher2Teacher Service)
Date: Mar 16, 1998 at 17:21:33
Subject: Re: Factoring and quadratics

Luis,

Quadratics can be applied to marketing. Suppose you are trying to decide how much 
you should charge for tickets to a concert. If the price is too low, every ticket 
will be sold. If the price is way out of line, then not every ticket will be sold.  
The problem is to determine at what price all tickets will be sold and what will 
be the maximum income generated.   

The number of tickets is a constant. Imagine doing some market research in which 
you find out that at $N only K tickets might be sold. For every $5 increase in 
ticket price it can be expected that 100 fewer tickets will be sold. Therefore, 
the revenue = the number of tickets sold multiplied by the cost per ticket. This 
is (K - 100x)($N + $5x). This gives you a quadratic equation. In factored form you 
can find the x-intercepts, and the average of these is the value of x that gives 
your the maximum revenue.   

I think that students aged 17-21 will relate to this type of problem. Ask them for
other similar situations. Perhaps they can find the $N amount for you.

Mary Lou

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