A small bed and breakfast, Babette's B&B, has seven bedrooms that can be rented. The owner, Babette, maintains a pristine establishment and rooms are in high demand. Thus, she can accept virtually as many bookings as she chooses. However, if she overbooks and everyone shows up, she must pay for any "overflow" guests to stay at the local chain hotel at a personal cost of $150. She makes $100 per night per room that is rented. Past experience has taught her that 25 percent of the guests who book rooms actually fail to show up a) Write down a function f(G), which gives the revenue that Babette will make as a function of G, the number of guests (rooms) that actually show up for any evening. Note that f(G) should increase at first as additional guests translate into additional revenue until the bed and breakfast is full. After that, the function should decrease as she has to pay for the "overflow" guests to stay elsewhere. b) If Babette accepts seven reservations for an evening (i.e., she does not overbook), what is her expected revenue? c) If Babette accepts eight reservations for an evening (i.e., she overbooks by one room), what is her expected revenue? d) Find the optimal overbooking policy. What is the expected revenue in this case? By how much does it exceed the expected revenue found in part (b) above when she does not overbook at all? e) If Babette can reduce the no-show rate from 25 percent to 12.5 percent (i.e., she can cut it in half) by calling guests two days in advance of their arrival date to confirm their reservation, what should the new policy be? What is the expected revenue in this case? How does it compare to that found in part (d)