A Firm with Market Power Faces the Following Estimated Demand $Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$

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