Refer to the Following:
a Firm with Market Power Faces $Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$

Refer to the following:
A firm with market power faces the following estimated demand and average variable cost functions:
$Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$
$A V C = 30 - 0.005 Q + 0.0000005 Q ^ { 2 }$
where
$Q _ { d }$ is quantity demanded, P is price, M is income, and
$P _ { R }$ is the price of a related good. The firm expects income to be $40,000 and
$P _ { R }$ to be $2. Total fixed cost is $100,000.
-What price should the firm charge in order to maximize profit?

A) $42.50
B) $48
C) $50
D) $62
E) $70