Refer to the Following:
a Firm Sells Two Goods (X

Refer to the following:
A firm sells two goods (X and Y) that are related in consumption. The estimated inverse demand and cost functions are:

$$\begin{array} { l } P _ { X } = 105 - 0.5 Q _ { X } - 0.75 Q _ { Y } \\P _ { Y } = 120 - Q _ { Y } - 0.5 Q ^ { 2 } \\M C _ { X } = 10 + 0.25 Q _ { X } \\M C _ { Y } = 16 + 0.5 Q _ { Y }\end{array}$$
-What are the profit-maximizing prices for the two goods?

A) $P _ { X }$ = $40, $P _ { y }$ = $32.50
B) $P _ { X }$ = $53.50, $P _ { y }$ = $61
C) $P _ { X }$ = $80, $P _ { y }$ = $55
D) $P _ { X }$ = $112.50, $P _ { y }$ = $87.75
E) none of the above