Question 894595
q for how many members
x for price


PRICE__________Members
300____________1000
302____________1000-5
304____________1000-10
.
{{{highlight_green(q=300-(5/2)x)}}}.  Member count is a function of price.


Let r stand for revenue.
{{{r=q*x}}}
{{{r=x(300-(5/2)x)}}}
or in general form for the function,
{{{highlight_green(r=-(5/2)x^2+300x)}}}


You want the maximum of this formula for r, the vertex.  Find the roots, check the value at the midpoint of the two roots and use it to compute r.