The cost, in dollars, for a company to produce x widgets is given by C(x) = 2025 + 7.8x for x >= 0, and the price-demand function, in dollars per widget, is p(x) = 24 - 0.018x for 0 <= x <= 1330.

(a) Find and interpret C(250).

(b) Find and interpret (average cost) C_(250). (Note that C_(x) is the average cost function.)

(c) Find and simplify the expression for the revenue function R(x). (work optional)

(d) Find and simplify the expression for the profit function P(x). (work optional) Note that p(x) and P(x) are different functions.

(e) Find and interpret P(250), where P(x) is the profit function in part (d).

(price-demand p, revenue R, cost C, average cost C_, and profit P )