Question 1111304
{{{ R(p) = -8p^2 + 48000p }}}
This has the general form:
{{{ y = a*x^2 + b*x + c }}}
( {{{ c=0 }}} )
The x-value of the vertex ( maximum in this case ) is:
{{{ x[v] = -b/(2a) }}}
For your problem:
{{{ p[v] = -48000/( 2*(-8)) }}}
{{{ p[v] = 3000 }}}
Plug this value back into the eqution
{{{ R[v] = -8*3000^2 + 48000*3000 }}}
{{{ R[v] = -8*9000000 + 144000000 }}}
{{{ R[v] = -72000000 + 144000000 }}}
{{{ R[v] = 72000000 }}}
At a unit price of $3,000, the maximum revenue is 
$72 million
check my math