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An eReader factory has revenues which follow the formula R=x squared + 2400x - 1,320,000, Where x is the number of eReaders sold each month. If the
factory had $80,000 in revenue last month and only has the resources to produce up to 1300 eReaders in a single month, how many eReaders were sold? Show all steps and answers

Sagot :

AL2006

If the revenue last month was 80,000, then

         80,000 = x² + 2,400x - 1,320,000

That's the only glimmer of intelligence required to answer this question.
The rest is all a matter of solving this quadratic equation.


Subtract 80,000 from each side:  x² + 2,400x - 1,400,000 = 0

This ugly thing may be factorable, but I'm not going to wander around
looking for factors.  I'm going straight to the quadratic formula.
With that, I get the solutions:

               x = -1200 + or - √2,840,000

               x = 485.2
and
               x = -2,885.2

The solution that has physical significance is the first one: 485 .


When I saw the requirement that the answer must be 1300 or less,
I expected to find that both solutions to the quadratic equation were
positive, and that one of them was greater than 1300.  But that didn't
happen.  485 (rounded) is the only positive solution.  That's my answer,
and I'm sticking to it.


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