The Type of Mathematics 25 Questions in Chongqing Senior High School Entrance Examination

A large hotel in Kaili has 100 private rooms. During the business hours of dinner every day, when the charge for each private room is 100 yuan, all private rooms can be rented out. The charge for each private room is increased by 20 yuan, reduced by 10, and the charge for each private room is increased by 20 yuan, reduced by 10, thus changing the method of increasing 20 yuan every time.

(1) If the charge of each room is increased by X (yuan), the income of each room will be y 1 (yuan), but the room rent will be reduced by y2. Please write the functional relationships among y 1, y2 and x respectively.

(2) In order to get more income with less investment, after each private room is increased by X (yuan), the hotel owner assumes that the total income of eating in private rooms every day is Y (yuan). Please write down the functional relationship between Y and X, and find out how much each private room needs to increase its dinner every day to get the maximum room rate income, and explain the reasons.

A computer company sells Type A computers. Due to the economic crisis, the price of computers continues to fall. In March this year, the price of computers was 1000 yuan lower than that of the same period last year. If you sell the same number of computers, the sales volume last year was 6.5438+0 million yuan, and this year's sales volume is only 80 thousand yuan.

(1) What was the price of a computer in March this year?

(2) In order to increase income, the computer company decided to resell the second model computer. It is known that the computer purchase price is 3500 yuan, and the computer purchase price is 3000 yuan. The company expects that the funds for purchasing these two computers will not exceed 50,000 yuan and not be less than 48,000 yuan. * * 65,438+05 units. How many purchase plans are there?

(3) If the price of computer B is 3,800 yuan each, in order to open up the market of computer B, the company decides to return cash yuan to customers for every computer B sold, so that all the schemes in (2) can get the same profit. What should the value be? At this time, which scheme is more beneficial to the company?

Due to the state's key support for energy-saving and environmental protection industries, the sales market of some energy-saving products is gradually picking up. At the beginning of this year, a dealer signed a purchase contract with the manufacturer, stipulating that the purchase price within one year was 0. 1.0000 yuan/set, and a deposit of 50,000 yuan was paid in advance. He plans to reach a certain sales volume within one year, and the total purchase amount and deposit used to complete this sales volume should be controlled at not less than 340,000 yuan, but not more than 400,000 yuan. If the relationship between the selling price (ten thousand yuan/set) and the number of months in a year (integer) is as follows, it is found that there is a changing trend between the actual monthly sales volume (set) and the number of months after a year.

(1) directly write down the actual monthly sales (units) and the number of times per month.

Function relation of;

(2) Find the actual monthly sales profit of the first three months and the current month (ten thousand yuan).

Functional relationship between degrees;

⑶ Try to judge which month of the year has the highest price, and point out the highest price;

Please calculate whether he has completed the sales planned at the beginning of this year.

A vegetable processing factory undertakes the task of processing vegetables for export, and a batch of vegetable products need to be packaged into cartons with certain specifications. There are two options for supplying this kind of cartons:

Option 1: Customized purchase from carton factory, with the price of 4 yuan per carton;

Scheme 2: The vegetable processing factory rents machines to process and manufacture this kind of cartons, and the machine rental fee is charged according to the number of cartons produced. The factory needs a one-time investment of 16000 yuan for machine installation, and the processing cost of each box is 2.4 yuan.

(1) If cartons of this specification are needed, please write down the functional relationship between the cost (yuan) of buying cartons from carton factory and the cost (yuan) of processing and manufacturing cartons in vegetable processing factory.

(2) Suppose you are the decision maker, which scheme do you think should be chosen? And explain why.

A station has a large passenger flow, and passengers often have to queue for a long time to buy tickets. According to the survey statistics, about 300 passengers queue up to buy tickets at the beginning of ticket sales every day, and new passengers are constantly entering the ticket office to queue up to buy tickets. The functional relationship between the number of new ticket buyers (persons) and the ticket selling time (minutes) is shown in the figure. The functional relationship between the number of votes (people) and time (minutes) in each ticket window is shown in the figure. The functional relationship between the number of people waiting in line at the ticket office on a certain day and the time (minutes) of ticket sales is shown in the figure. It is known that two ticket sales windows were opened in the first minute of ticket sales.

( 1);

(2) The number of passengers queuing at the ticket office at the 60th minute of ticket purchase;

(3) In studying and practicing Scientific Outlook on Development activities, the station decided to add a ticket window based on the principle of "people-oriented, convenient for passengers". If all the passengers queuing to buy tickets can buy tickets within half an hour after the ticket sales start, so that the passengers arriving at the station in the future can buy them at any time, please help us calculate how many ticket sales windows should be opened at least at the same time.

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