Question 833705
Find the p value for the vertex and then and use it to compute R.  You may also want to try completing the square to put R into standard form.


{{{highlight(highlight(P<>p))}}}


A process for finding p of the vertex:
{{{-15p^2+300p+12000=0}}}, because this is a way to find the p intercepts, assuming p is on a horizontal number line...
Divide both sides by 15...
{{{-p^2+20p+800=0}}}
{{{(-1)(p^2-20p-800)=0}}}
{{{(-1)(p-40)(p+20)=0}}}
The p intercepts are -20 and 40.  The middle value of this is {{{highlight_green((-20+40)/2=highlight(10))}}}.  This means that the vertex occurs at {{{highlight(p=10)}}}.
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The maximum revenue, {{{highlight(R=-15*10^2+300*10+12000)}}}