If a group of new meeting guests in Huanghai hotel are arranged to live in a standard room with 2 people in each room, they need 18 rooms. The waiter finds that the standard room is full, How many rooms should we arrange?

If a group of new meeting guests in Huanghai hotel are arranged to live in a standard room with 2 people in each room, they need 18 rooms. The waiter finds that the standard room is full, How many rooms should we arrange?

2X18=36
36/(2+1)=12
12 rooms should be arranged

There are 120 guest rooms in a hotel. When the daily rent of each room is 50 yuan, it is full every day. The rent should be increased after decoration
There are 120 guest rooms in a hotel. When the daily rent of each guest room is 50 yuan, it is full every day. After the decoration of the travel agency, the rent should be increased. According to the market survey, every 5 yuan increase in the daily rent of a guest room will reduce the daily rent of six guest rooms. In order to maximize the total income of the daily rent of the guest room, the daily rent of each guest room will be increased to - yuan

Suppose to increase x yuan, income y yuan
y=（120-6/5x)(50+x)
=6000+60X-6/5X2
=-6/5(x2-50X-5000）
=-6/5(x-25)2+6750
When x = 25, the maximum value of Y is 6750 yuan
Daily rent increased to: 50 + 25 = 75 yuan
At this time, the income is the highest

There are 120 guest rooms in a hotel. The daily rent of each room is 50 yuan, which is full every day. After the hotel is decorated, the rent should be increased. According to market research, if the daily rent of a guest room increases by 5 yuan, the number of rooms will be reduced by 6. Regardless of other factors, when the hotel increases the daily rent of each guest room to how much yuan, the total income of the daily rent of the guest room is the highest? How much more than the total daily rental income before decoration? (with necessary explanation)

If the daily rent of each room is increased by x 5 yuan, and the total daily rent income is y yuan, then every 5 yuan increase in the daily rent of a room will reduce the number of rooms rented per day by 6. The daily rent is (50 + 5x) yuan, and the number of rooms is (120-6x). From the profit = daily rent × number of rooms, y = (50 + 5x) (120-6x), that is, y = - 30 (X-5) 2 + 6750. When x = 5, ymax = 6750, that is, the hotel When the daily rent of each guest room is increased to 75 yuan, the total income of daily rent of guest room is the highest, and the total income of daily rent is 6750-120 × 50 = 750 yuan