suppose a firm has the total cost function

C(Q)=100+2Q+(1/2)Q^2

a)find the firm's marginal cost function

b) find the firm's average total cost function

c)the fact that the total cost function takes the value 100 at Q=0 tells you something about variable cost. find the firm's average variable cost function.

d) suppose production price is 20. the firm views that price as beyond its control. how much will the firm produce if it wants to maximize profit ?

e) now suppose price continues to be 20 and suppose the government imposes a tax of T dollars(to be paid by firm) on every unit the firm produces. what values of T must the government avoid if it wants to collect any tax revenue at all?(continue to assume that the firm choose its product quantity so as to maximize profit)