Answer
$P=-0.5p^{2}+2800p-3,320,000$
Maximum profit is ${{\$}} 600,000$ when the hourly fee is ${{\$}} 2800$ per hour.
Work Step by Step
$ P=R-C\quad$(use the results of b and c.)
$P=-0.5p^{2}+2000p-(-800p+3,320,000)$
$P=-0.5p^{2}+2800p-3,320,000$
The graph is a parabola, opening down.
The maximum profit occurs at the vertex, when $p=-b/(2a)$
$p=-\displaystyle \frac{2800}{-2\times 0.5}= {{\$}} 2800$ per hour.
The corresponding profit is
$P=-0.5(2800 )^{2}+2800(2800)-3,320,000$
$={{\$}} 600,000$
