A Price-Setting Firm Faces the Following Estimated Demand and Average $Q _ { d } = 800,000 - 2,000 P + 0.7 M + 4,000 P _ { R }$

A price-setting firm faces the following estimated demand and average variable cost functions: $Q _ { d } = 800,000 - 2,000 P + 0.7 M + 4,000 P _ { R }$ $A V C = 500 - 0.03 Q + 0.000001 Q ^ { 2 }$ where $Q _ { d }$ is the 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 $53.Total fixed cost is $2,600,000.What price should the firm charge in order to maximize profit?

A) $356
B) $400
C) $420
D) $445
E) $510