The Quantity Q of Zeng Athletic Shoes Which Are Sold $f ^ { \prime } ( 150 ) = - 100$

Essay

The quantity q of Zeng Athletic Shoes which are sold depends on the selling price p. [That is, q = f(p).]
(a) If you know that f (150) = 14,000, what can you say about the sale of these shoes?
(b) If you know that $f ^ { \prime } ( 150 ) = - 100$ , what does that tell you about the sale of these shoes?
(c) The total revenue, R, earned through the sale of Zeng shoes is given by $R = p \cdot q$ . Find $\frac { d R } { d p } \text { when } p = 150$ (d) Suppose that the shoes are currently priced at $150. What effect will lowering the price likely have on the total revenue? Justify your answer.