Answer
$P=-10p^{2}+430p-4200$
Maximum profit is ${{\$}} 422.50$ when entrance fee is ${{\$}} 21.50$.
Work Step by Step
$P=R-C\quad $, use the results of parts b and c.
$P=-10p^{2}+430p-4200$.
The graph is a parabola, opening down.
The maximum profit occurs at the vertex, when $p=-b/(2a)$
$p=-\displaystyle \frac{430}{-2\times 10}= {{\$}} 21.50$
The corresponding profit is
$P=-10(21.50)^{2}+430(21.50)-4200$
$={{\$}} 422.50$
