You sell a "commodity" in a market that resembles perfect competition, and your cost function is C(Q) = 2Q + 3Q^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 70 percent chance the market price will be $200 and a 30 percent chance it will be $600.
Find the output you should produce in order to maximize your expected profits so that you can then determine your expected profits accurately.