Math 165 HW 8 Due Thursday, March 31st at 11:59pm in Gradescope 1. A hotel with 300 rooms is filled to capacity every night if they charge 880 per room per night. For each $1 increase in room rental rate, they rent out 3 fewer rooms per night. Each rented room also costs the hotel $10 to service each morning. First, construct a Profit function using x= number of room rate increases. Then complete the following: a) The new price per room each night b) How many rooms will be rented each night e) Maximum Profits per night