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 homes before you learn how strong demand is for homes in this large neighborhood. There is a 80 percent chance of low demand and a 20 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 300,000-300Q and P= 800,000 -200 Q, respectively. Your cost function is aQ)= 180,000+ 260,000Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: 250 homes Profits you can expect: $