The demand function for a Christmas music CD is given by $$Q = 0.25(225-p^2)$$ where $Q$ (measured in units of a hundred) is the quantity demanded per week and $p$ is the unit price in dollars.

(a) Evaluate the demand elasticity $E$ when $p=10$.
$E(10)=$

Here, "demand elasticity" is the absolute value of $\displaystyle \frac{\text{percent change in quantity}}{\text{percent change in price}}$ for an infinitesimal change in price, so $$E = \left| \lim_{\Delta p \to 0} \frac{ \Delta Q / Q}{\Delta p / p} \right| \ .$$

(b) Should the unit price be lowered slightly from 10 to increase revenue? ?? Yes No

(c) When is the demand elasticity unitary?
$p=$ dollars

(d) Find the maximum revenue.
Maximum revenue = hundreds of dollars