The profit earned producing shirts is given by the function $P(x)=-0\mathrm{.}002x^2+20x-200,$ where $x$ is the number of shirts produced.

a$.$ If we produce $1000$ shirts, what is the profit?

b$.$ If we produce $1000$ shirts, what is the average profit per shirt?

c$.$ If we produce $200,000$ shirts, what is the average profit earned per shirt?

d$.$ Find the average profit function $\frac{?}{\text{b}\text{a}\text{r}}(P)(x)$ from producing shirts.

e$.$ Does it make sense to talk about how average revenue behaves as quantity gets large?