A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?

A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?

(1) From the question meaning: y = 60-x10 (2 points) (2) z = (200 + x) (60-x10) = - 110x2 + 40x + 12000 (3 points) (3) w = (200 + x) (60-x10) - 20 × (60-x10) (2 points) = - 110x2 + 42x + 10800 = - 110 (x-210) 2 + 15210. When x = 210, w has the maximum value