The function P$($x$)=-3\mathrm{.}25$x$^2+1400$x$-5500$ gives the profit when x units of a certain product are sold. Find

a$)$ the profit when $70$ units are sold

$$ dollars

b$)$ the average profit per unit when $70$ units are sold

$$ dollars per unit

c$)$ the rate that profit is changing when exactly $70$ units are sold

$$ dollars per unit

d$)$ the rate that profit changes on average when the number of units sold rises from $70$ to $140.$

$$ 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