Example: Assume that a demand equation is given by P = -0.01x +50 dollars per unit when * units are sold, and the cost of producing * units is given by C(x) = 3000 -20x + 0.03x dollars. (a) Find the revenue function, R (x ) . (b) Find the instantaneous rate of change of revenue (marginal revenue) for the following production levels (values of * ). (i) 500 units (ii) 1000 units 6 (c) Find the profit function, P(x). (d) Find the instantaneous rate of change of profit (marginal profit) for the following production levels (values of x ). (i) 500 units (ii) 1000 units (e) When is the marginal profit zero