Assume that a demand equation is given by q = 5000 - 100p.
(a) Find the revenue function, R(q), and the marginal revenue function, R′(q).
(b) Find and interpret the marginal revenue for q = 500 units.
(c) Find and interpret the marginal revenue for q = 1000 units.
Suppose that the cost of producing q units is given by
C(q) = 3000 - 20q + 0.03q².
(d) Find the marginal profit function.
(e) Find and interpret the marginal profit when the production is q = 500 units.
(f) At what level of production will the profit be $0 for producing an extra unit?