You are the manager of a firm that sells a commodity in a market that resembles perfect competition, and your cost function is
\(C(Q) = Q + 2Q^{2}\)
Unfortunately, due to production lags, you must make your output decision prior to knowing for certain the price that will prevail in the market. You believe that there is a 60 percent chance the market will be $100 and a 40 percent chance the market will be $200.

a. Calculate the expected market price.

b. What output should you produce in order to maximize expected profits?

c. What are your expected profits?