The price-demand and cost functions for the production of microwaves are given as $$p = 295 - \frac{x}{90}$$ and $$C(x) = 80000 + 40 x,$$ where $x$ is the number of microwaves that can be sold at a price of $p$ dollars per unit and $C(x)$ is the total cost (in dollars) of producing $x$ units.

(A) Find the marginal cost as a function of $x$.
$C'(x)$ =

(B) Find the revenue function in terms of $x$.
$R(x)$ =

(C) Find the marginal revenue function in terms of $x$.
$R'(x)$ =

(D) Evaluate the marginal revenue function at $x = 1500$.
$R'(1500)$ =

(E) Find the profit function in terms of $x$.
$P(x)$ =

(F) Evaluate the marginal profit function at $x = 1500$.
$P'(1500)$ =

Hint: