SOLUTION: A car rental agency rents 200 cars per day at a rate of $30 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce a maxi

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Question 809873: A car rental agency rents 200 cars per day at a rate of $30 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce a maximum income? What is the maximum income?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Starting income, 200%2A30 dollars per day.
The 1 dollar rate per day increase (price) does this:
%28200-5%2Ax%29%2830%2Bx%29 for the income per day.

Not given if that income is revenue or profit, so it might simply be called, y:
highlight%28y=%28200-5x%29%2830%2Bx%29%29, and we might expect x to be whole numbers, although might not need such a restriction.

The equation is quadratic and has a maximum, which is what we are asked to find.

Consider the zeros of y. They occur at x=40 and x=-30. Do not worry about any x%3C0, because they would not be actual values of x; they would be hypothetical only. We want the x value exactly in the middle of 40 and -30.

Max x is at %2840%2B%28-30%29%29%2F2=10%2F2=highlight%285%29.
This means that the rental rate should be 30%2B5=highlight%2835%29 dollars.