Senior one math required 1 function application problem.
1. Cut a 20 cm long iron wire into two sections and make a square around the length of each section of iron wire, then the minimum value of the sum of the areas of these two squares is cm2.
2.(20 10 Liaocheng guanxian Experimental Middle School Model 2) The original price of a commodity was 289 yuan, and the price was 256 yuan after two consecutive price reductions. If the average percentage of each price reduction is x, then the following equation is correct _ _ _ _ _ _ _ _ _ _ _ _.
Build a rectangular chicken farm with a 48-meter-long bamboo fence. One side of the chicken farm is brick, the other three sides are surrounded by bamboo fences, and a 2-meter-wide door (no fence) is opened on the opposite side of the brick wall. When the side length of a chicken farm is several meters, which chicken farm occupies the largest area? What is the maximum area?
4. When shopping malls sell a batch of shirts, they can sell an average of 20 shirts a day, and each shirt is profitable in 40 yuan. In order to expand sales, increase profits and reduce inventory as soon as possible, the mall decided to take price reduction measures. After investigation, it is found that if each shirt is reduced by 1 yuan, the mall can sell 2 shirts on average a day. (1) If each piece is reduced by X yuan, the daily profit will be Y yuan. Find the relationship between Y and X (3) How much is the price reduction of each shirt, and the daily profit of the shopping mall is the largest? What's the profit?
There are 60 rooms in the hotel housekeeping department for tourists to live in. When the price of each room is 200 yuan per day, the room will be full. If the price of each room increases by 10 yuan every day, one room will be free. There are rooms for tourists, and the hotel needs to pay various fees for each room in 20 yuan every day. Let the price of each room increase by X yuan every day.
The daily occupancy rate of (1) room is a function of y (room) and x (yuan).
(2) The daily room rate of this hotel is a function of z (yuan) and x (yuan).
(3) The functional relationship between the daily profit of the hotel housekeeping department W (yuan) and X (yuan); What is the maximum value of W when the price of each room is several yuan per day? What is the maximum value?
6. A store deals in a batch of small commodities imported from 2 yuan. In the process of marketing, it is found that if the goods are sold in 3 yuan at the lowest price, the daily sales volume is 18 pieces. If the unit price increases by 1 yuan, the daily sales volume will decrease by 2 pieces. Let the sales unit price be X (yuan) and the daily sales volume be Y (pieces).
(1) Write the functional relationship between the daily sales volume y (pieces) and the sales unit price x (yuan); (2) Let the daily sales gross profit (gross profit = total sales-total purchase) be p (yuan), and find the functional relationship between gross profit p (yuan) and sales unit price x (yuan);
(3) Draw a sketch of the function image of P relative to X in the coordinate system shown below, and mark the coordinates of vertices; (4) Observe the image and tell me what the gross profit of daily sales is when the sales unit price is RMB. how much is it?
7.(08 Liangzhou) There is an edible wild mushroom in our state. At the time of listing, Li, the foreign manager, bought the wild mushroom 1000 kg at the market price of 20 yuan/kg and stored it in the cold storage. It is predicted that the market price of this wild fungus will increase by 1 yuan per kilogram every day; The total daily cost of freezing these wild mushrooms is 3 10 yuan, and the wild mushrooms can be stored in the cold storage at most 160 yuan. At the same time, an average of 3 kilograms of wild mushrooms are damaged every day and cannot be sold.
(1) Let the market price of this wild fungus per kilogram be Y yuan after X arrives, and try to write the functional relationship between Y and X. 。
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(2) If this batch of wild mushrooms is sold once after being stored for x days, let the total sales amount of this batch of wild mushrooms be P yuan, and try to write the functional relationship between P and X. 。
(3) How many days will Manager Li store these wild mushrooms before selling them, so as to get the maximum profit of W yuan? (Profit = total sales-acquisition cost-various expenses)
8.(09 Changsha, Hunan) In order to support college students' entrepreneurship, the municipal government provided an interest-free loan of 800,000 yuan for a college student to start a company to produce and sell an electronic product independently developed, and agreed to gradually repay the interest-free loan with the profits of the company. It is known that the production cost of this product is 2,500 yuan per 40 yuan, the monthly salary of each employee is 2,500 yuan, and the company has to pay other expenses of 6,543.8+0.5 million yuan per month. The monthly sales volume of this product is Y (ten thousand pieces).
(1) Find the functional relationship between monthly sales y (ten thousand pieces) and sales unit price x (yuan);
(2) When the sales unit price is set as 50 yuan, how many employees can the company arrange to ensure that the company's monthly profit reaches 50,000 yuan (profit = sales-production cost-employee salary-other expenses)?
(3) If the company has 80 employees, the company can pay off the interest-free loan in a few months at the earliest?
9.(09 Chengdu) University graduates respond to the country? Start your own business? At our call, we invested in a jewelry store. The store bought a new jewelry which was put on the market this year. The trial sale lasted for 30 days, and the purchase price was 20 yuan/piece. After the sale, we learned that there is the following relationship between daily sales P (number of pieces) and sales time X (days): P=-2x+80( 1? x？ 30, and x is an integer); It is also known that the sales price in the first 20 days of Q 1 (yuan/piece) has the following relationship with the sales time X (day): Q 1? x？ 30 ( 1? x？ 20, and X is an integer), the sales price Q2 (yuan/piece) of the last 10 day has the following relationship with the sales time X (day): Q2=45(2 1? x？ 30 and x is an integer).
(1) Try to write the functional relationship between the daily sales profit R 1 (yuan) in the first 20 days and the daily sales profit R2 (yuan) in the latest 10 day and the sales time x (days) respectively;
(2) In the 30-day trial sale, which day has the largest daily sales profit? Find this maximum profit. Note: Sales profit = sales revenue-purchase cost.
10. The cost of a seasonal commodity produced by Red Star Company is 20 yuan. Through market research, it is found that the relationship between the daily sales volume m (pieces) and the time t (days) in the next 40 days is as follows:
In the next 40 days, the functional relationship between the daily price y 1 (yuan/piece) and the time t (day) of the previous 20 days is y 1?
(1) Carefully analyze the data in the above table, and use the knowledge of the learned linear function, quadratic function and inverse proportional function to determine the relationship between m (piece) and t (day) that satisfy these data;
(2) Please predict which day will have the largest daily sales profit in the next 40 days, and what is the maximum daily sales profit?
(3) In the first 20 days of actual sales, the company decided to donate one yuan of profit for each commodity sold (A
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