A new hotel in Orlando is ready to open for business. In a small, simple economy it is reasonable to assume that if the price of an item (such as a hotel room) is too high, then there will be a drop in profit for the hotel, as guests will not be willing to book a room. Likewise, it is reasonable to assume that if the price of a hotel room is too low, then there will also be a drop in profit, as some potential guests may have doubts and questions as to why the hotel room is so 'cheap'.  From a business perspective, there is always a sweet spot in which the price isn't too high or too low and result in maximum profit. With this idea in mind, I'd like you to consider the following scenario.  The Hotel Orlando has 115 rooms, which are rarely all full during the off season. Hotel records show that at $46 per night, they average 81 occupied rooms during the off season, but for every $2 increase in the room rate, 3 more rooms remain vacant. The owners would like to know what rate to charge future guests in order to maximize their revenue from the hotel. For this scenario, let x represent the number of $2 price increases. Develop a quadratic model for the nightly revenue R(x) at the Hotel Orlando, and then use your model to determine the maximum nightly revenue the hotel can generate and the optimum room rate to charge. ​