Let $R(x),C(x),$ and $P(x)$ be$,$ respectively, the revenue, cost, and profit, in dollars, from the production and sale of $x$ items. If $R(x)=8x$ and $C(x)=0\mathrm{.}003x^2+4\mathrm{.}3x+70,$ find each of the following.

a$)P(x)$

b$)R(100),C(100),$ and $P(100)$

c$)R^{\text{'}}(x),C^{\text{'}}(x),$ and $P^{\text{'}}(x)$

d$)R^{\text{'}}(100),C^{\text{'}}(100),$ and $P^{\text{'}}(100)$