- This is a type of problem that students often encounter in
calculus classes! But we can solve it by applying a little common
sense, a little patience, and (if we want to prove that our answer is
correct)
a little algebra.
- First, let's make sure we understand what is going on in the
problem.
At first our analyst is selling 500 newsletters at $10 each, for an
income
of $5,000.
- Now suppose she increases the price of the newsletter to $11.
According
to the problem, she would then lose 8 subscribers. So she'll only sell
492
newsletters. But her income will now be $11 x 492 = $5,412.
- Of course, she can't increase the price too much, or no one
will
buy it, and she won't make any money.
- You can try various prices to figure out for what price her monthly
income is as big as possible.
As always, be sure to explain the
work you did to arrive
at your answers!
A stock market analyst sold a monthly newsletter to 500 subscribers at
a price of $ 10 each. She discovered that for each $0.25 increase in the
monthly price of the newsletter, she would lose 2 subscriptions. For what
price should she sell each issue to bring in the greatest total monthly
income?