Guntern Corp is a monopoly company producing goods in Switzerland. Based on its observation on the current uncertainty surrounding the economy due to the recent pandemic, there is a 50% chance the firm's demand curve will be P= 20-Q and a 50% chance it will be P= 100-Q. The MC (marginal cost) of the firm is MC=4Q.

a. Derive the expression for the expected marginal revenue function for the firm

b. What is the firm's expected profit-maximizing quantity?

c. What is the firm's expected profit-maximizing price?

d. What is the expected total profit of the firm?