As the manager of Smith Construction you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the new homes before you learn how strong demand is for homes in this large neighborhood. There is a 50 percent chance of low demand and a 50 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 200,000 250Q and P =400,000 -250Q, respectively. Your cost function is C(Q) = 110,000 + 200,000Q. How many new homes should you build, and what profits can you expect?