Assume that the price, in dollars, of a sound system is given by

where q represents the demand for the product.
(a) Find the revenue function, R(q), and the marginal revenue function, R′(q).
(b) Find and interpret the marginal revenue when the demand is 10 systems. 

Suppose the cost of producing q sound systems is given by 

C(q) = 0.4q² + 160q + 50.
(c) Find the marginal profit function, P′(q).
(d) Find and interpret the marginal profit when the demand is 10 systems.

Transcribed Image Text:

p(q) = = 1000 9² + 1000,