Before the NHL season begins,the Montreal Canadiens choose the number of (expected) wins they are going to get that season by constructing a roster of players.Fans enjoy wins, but the additional revenue of each win is decreasing and given by the following average revenue (inverse demand) curve:

AR(W) =P(W) = 2102W

It is costly to increase the number of wins because the team has to acquire better talent. The cost of an additional win is increasing with the number of wins:

MC(W) = 30 +W

The total number of games in a regular NHL season is 82.

a)Find the Canadiens marginal revenue curve, MR(W).

b)If the Canadiens objective is to maximize profits, how many wins W* are chosen?

c)If the Canadiens objective is to maximize the number of wins, how many wins W** are chosen?

d)Repeat b) and c) if the total number of games in the NHL season is reduced to 56.