Chapter 11.5, Problem 11E

In Problems 11 and 12, the demand functions for specialty steel products are given, where p is in dollars and q is the number of units. For both problems

(a) find the elasticity of demand as a function of the quantity demanded, q.

(b) find the point at which the demand is of unitary elasticity and find intervals in which the demand is inelastic and in which it is elastic.

(c) use information about elasticity in part (b) to decide where the revenue is increasing, where it is decreasing, and where it is maximized.

(d) use the graph of the revenue function $R=pq$ to find where revenue is maximized. Is it at the same quantity as that determined in part (c)?

$p=120\sqrt[3]{125-q}$