The cost (in thousands of dollars) of producing x thousand units of Acrosonic loudspeaker systems is: TC = 12X^2 + 50X + 3. Price p (in $ per unit) and quantity demanded x (in thousand units), which are both required to be non-negative, are related as: p = 170 - 3x .

(a) Find the marginal cost (MC) function.

(b) Find marginal revenue (MR) as a function of output.

(c) Find the profit as a function of output.

(d) What quantity maximizes profit, and how much is that profit?