1. The revenue received by a firm that sells x 0 units of output is R(x) = 144xx 2 , while the cost of producing x units is C(x) = 1 3 x 3 6x 2 + 160x.

(a) Find the C (x) (often called "marginal cost" in economics). Show that C (x) is always positive.

(b) Show that the profit function is (x) = 1 3 x 3 + 5x 2 16x. [Hint: profit = revenue cost]

(c) Find the value of x that maximizes profits. Explain your answer.

(d) Draw the profit function (x) over the relevant domain of x, and label the extreme points (maxima/minima).