Question 809873
Starting income, {{{200*30}}} dollars per day.
The 1 dollar rate per day increase (price) does this:
{{{(200-5*x)(30+x)}}} for the income per day.


Not given if that income is revenue or profit, so it might simply be called, y:
{{{highlight(y=(200-5x)(30+x))}}}, 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<0}}}, 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 {{{(40+(-30))/2=10/2=highlight(5)}}}.
This means that the rental rate should be {{{30+5=highlight(35)}}} dollars.