The function $P(x)=-3\mathrm{.}5x^{2}2025x-5000$ gives the profit when $x$ units of a certain product are sold. Find

a$)$ the profit when $85$ units are sold

$$ dollars

b$)$ the average profit per unit when $85$ units are sold

$$ dollars per unit

c$)$ the rate that profit is changing when exactly $85$ units are sold

$$ dollars per unit

d$)$ the rate that profit changes on average when the number of units sold rises from $85$ to $170.$

$$ dollars per unit

e$)$ The number of units sold when profit stops increasing and starts decreasing. $($Round to the nearest whole number if necessary.$)$

$$ units