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 demand and cost conditions are:
$$\begin{array} { l } P _ { X } = 20 - 0.1 Q _ { X } - 0.05 Q _ { y } \\P _ { y } = 70 - 0.3 Q _ { y } - 0.1 Q _ { X } \\M C _ { X } = 1 + 0.1 Q _ { X } \\M C _ { y } = 2 + 0.25 Q _ { y }\end{array}$$
-What are the profit-maximizing levels of output for the two goods?

A) $Q _ { x }$ = 20, $Q _ { Y }$ = 10
B) $Q _ { x }$ = 41, $Q _ { Y }$ = 24
C) $Q _ { x }$ = 56, $Q _ { Y }$ = 24
D) $Q _ { x }$ = 51, $Q _ { Y }$ = 74
E) none of the above