Special training of scheme design in inequality

1. (Qingdao, Shandong, 2007) A beverage factory developed two new drinks A and B, the main raw materials are both A and B.

It's in every bottle of drinks. The content of B is shown in the following table. First, 2800g of raw material A and 2800g of raw material B were used for testing.

Production: It is planned to produce two kinds of drinks, A and B 100 bottles, with X bottles of drink A, and answer the following questions.

Jiayi

A piece of 20 grams, 40 grams.

30 grams 20 grams

(1) How many production schemes are there? Write the solution process.

(2) If the cost of a drink per bottle is 2.60 yuan and the cost of B drink is 2.80 yuan, these two drinks

The total cost of drinks is y yuan. Please write the relationship between y and x and explain what the value of x will be.

The lowest total cost?

2. A town in our city organized 20 vehicles to load 100 tons of three kinds of ABC3 navel oranges for sale in other places. According to the plan, 20 cars will be transported, and each car can only transport the same navel orange. And must be fil. According to the information provided by the next Olympic Games. Answer the following questions

Navel orange variety ABC

Vehicle weight per vehicle (ton) 654

Get (100 yuan) 12 16 10 per ton of navel orange.

(1) Let the number of vehicles carrying A navel orange be X and B navel orange be Y, and find the functional relationship of X and Y..

(2) If each navel orange carries no less than 4 vehicles, what is the arrangement of which vehicle? And write out each layout.

(3) What kind of sales plan should be adopted to maximize the profit of this sale? And find the maximum profit value.

3. In 2007, in preparation for the 20th anniversary celebration of a county in our city, the county celebration garden department decided to use the existing 3,490 spray flowers to place 2,950 pots of B flowers with AB2 gardening ***50 on both sides of Yingbin Avenue, 80 pots of A flowers, 40 pots of B flowers and 50 pots of B flowers.

(1) The extracurricular activity group of Class 1, Grade 9 of a school undertook the design of this gardening modeling collocation scheme. How many matching schemes are there? Please help design it.

(2) Matching a Type A to 800 yuan and a Type B to 960 yuan shows that the one in No.1 Middle School has the lowest cost. how much is it?

4. (Nanchong, 2007) A shopping mall needs to purchase a batch of TV sets and washing machines. According to market research, it is decided that the purchase amount of TV sets should not be less than half of that of washing machines. The purchase price and selling price of TV sets and washing machines are as follows:

Classified TV washing machine

Purchase price (RMB/set) 1800 1500

Price (RMB/set) 2000 1600

It is planned to purchase *** 100 TV sets and washing machines, and the store can raise funds at most 16 1800 yuan.

(1) Could you please help the store calculate how many kinds of purchase plans there are? (excluding other expenses except the purchase price)

(2) After the store sells the purchased TV sets and washing machines, which purchase scheme will get the most profit? And seek the maximum profit (profit = selling price-buying price)

5. (Meishan, Sichuan, 2007) In response to the call of "building an environment-friendly and energy-saving society", a county decided to subsidize some towns and villages to build a number of biogas digesters, so that farmers can use economic and environmental protection biogas energy. There are 264 villagers in Happiness Village, and the government subsidizes the village by 340,000 yuan. The insufficient part was raised by villagers to build 20 type A and type B biogas digesters. The construction cost, available households and construction land of the two biogas digesters are as follows.

Construction cost of biogas digester (10,000 yuan/set) Available households (household/set) Covered area (square meter/set)

Type a 3 20 48

Type b 2 3 6

The relevant government departments granted 708 square meters of land for the construction of biogas digesters, and built X A-type biogas digesters. The cost of building two A-type biogas digesters was Y million yuan.

(1) Find the functional relationship between y and x.

(2) How many construction plans do not exceed the land area approved by the government to build biogas digesters, so that every villager in the village can use biogas?

(3) If every villager raises funds in 700 yuan on average, can the maintenance scheme with the lowest cost be satisfied?

6. A construction company urgently needs 230 tons of ordinary cement and 0/68 tons of steel, and there are 40 A and B trucks available. Each A-type truck can hold up to 6 tons of ordinary cement and 4 tons of steel, and the freight is 190 yuan. Each B-type truck can hold up to 5 tons of ordinary cement and 5 tons of steel, and the freight is 200 yuan.

(1) How many schemes are there to arrange two types of trucks, A and B?

(2) Which transportation scheme is the most economical? Why?

Type a freight car type b freight car

Commercial cement steel cement steel

Load/(ton/vehicle) 6 4 5 5

Number of trucks/vehicle

Total weight (ton)

Freight/(RMB/vehicle) 190 200

7. In order to celebrate the completion of the new school building, the school printed many commemorative books. Each book needs 10 8k paper, of which 4 are color pages and 6 are black and white pages. The total cost of printing this commemorative album consists of plate-making fee and printing fee. The plate-making fee has nothing to do with the print run, and the price is: 300 yuan for color pages and 50 yuan for black and white pages. The relationship between printing cost and print run is shown in the table below:

Print quantity a (in thousands) 1≤A \u 55≤A≤ 10

Color (unit: Yuan/sheet) 2.2-2.0

Black and white (unit: yuan/sheet) 0.7 0.6

(1) The plate-making fee for printing this commemorative album is RMB.

(2) If 2000 copies are printed, how much will * * * cost?

(3) If the school wants to print at least 4,000 copies, and the total cost is at most 60,000 yuan, find the range of print runs. (accurate to 0.0 1 1000)

8. (Chengdu, 2007) Class 3, Grade 9 of a school sent two students, Xiao Lin and Xiao Ming, to the supermarket near the school to buy pens as prizes to carry out a class meeting on the theme of "Welcome to the 2008 Beijing Olympic Games". Knowing that every Jinjiang brand pen 8 yuan and every Hongmei brand steel 4.8 yuan in the supermarket, I want to buy 40 of these two kinds.

(1) How many pens can each of them buy if both of them bring 240 yuan and spend it on prizes?

(2) Xiao Lin and Xiao Ming make sure that the number of Jinjiang brand pens they buy is less than that of Yu Hongmei brand pens, but many of them are Yu Hongmei brand pens. If they buy Jinjiang brand pens, they spend RMB.

(1) Please write the functional relationship between (element) and (branch) and find out the range of independent variables;

(2) Please help them figure out how many pens each of these two kinds cost, and how much did they spend at this time?

9. There are five fewer rooms on the first floor of the hotel than on the second floor, and there are 48 people in a tour group. If all rooms are arranged on the first floor, and there are 4 people in each room, the room is not enough; If there are 5 people in each room, some rooms are full of 5 people; And if all are arranged on the second floor and there are 3 people in each room, the room is not enough; If there are four people in each room, some rooms are full of four people. How many rooms are there on the first floor of the hotel?

10. A factory has 360 kilograms of raw materials A and 290 kilograms of raw materials B. It is planned to produce 50 products A and B with these two raw materials. It is known that it takes 9 kilograms of raw materials A and 3 kilograms of raw materials B to produce a product, which can make a profit in 700 yuan; To produce a type B product, 4 kg of type A raw materials and 10 kg of type B raw materials are needed, and the profit can be 1.200 yuan.

(1) What is the planned number of production pieces of products A and B? Please design it;

(2) The total profit of producing products A and B is Y (yuan), and the number of pieces produced by one product is X. Try to write the relationship between Y and X, and explain which production scheme has the largest total profit in (1). What is the maximum profit?

1 1, 200 tons of chemical fertilizer in city a and 300 tons of chemical fertilizer in city b. Now it is necessary to transport the fertilizer to rural areas C and D. If the freight rates from city A to rural areas C and D are 20 yuan/ton and 25 yuan/ton respectively, the freight rates from city B to rural areas C and D are 15 yuan/ton and 22 yuan/ton respectively.

12. In order to promote the development of freshwater aquaculture, a certain place controlled the price of freshwater fish between 8 yuan and 14 yuan, and decided to provide government subsidies for freshwater fish farming. Suppose the market price of freshwater fish is X yuan/kg. The government subsidy is NT$ per kilogram. According to the investigation, in order to make the daily supply of freshwater fish in the market completely equal to the daily demand, t and x should satisfy the equation 100 (X+T-8) = 270-3x. What is the minimum government subsidy to keep the market price below 10 yuan/kg?

13. (Linyi, Shandong Province, 2007) According to the market demand, a construction machinery factory plans to produce 100 large excavators of type A and type B. The production fund raised by the factory is not less than 224 million yuan, but not more than 225 million yuan, and all the funds raised are used to produce these two excavators. All the excavators produced can be sold.

Model A B

Cost (ten thousand yuan/set) 200 240

Price (RMB 10,000/set) 250,300.

1) What kind of production plan does this factory have for these two types of excavators?

(2) How can the factory get the maximum profit from production?

(3) According to the market survey, the price of each type B excavator remains unchanged, while the price of each type A excavator increases by million yuan (m > 0). How should the factory produce in order to get the maximum profit? (Note: Profit = selling price-cost)

14. (Mianyang, Sichuan, 2007) RoyceWong, a fruit grower in Jiangyou Baiyu Village, a "national civilized village" in Mianyang City, harvested 20 tons of loquat and 0/2 tons of peaches. At present, it is planned to rent eight A and B trucks and transport all these fruits to other places for sale. It is known that A truck can hold 4 tons of loquat and 1 ton of peach, and Otsuichi truck.

(1) How does RoyceWong arrange for A and B trucks to be transported to the sales place at one time? How many schemes are there?

(2) If the transportation cost of each class A truck is 300 yuan and the transportation cost of each class B truck is 240 yuan, which scheme does the fruit farmer choose to have the smallest transportation cost? What's the lowest freight?

15. In order to meet the needs of market economy, an enterprise decided to adjust its personnel structure. Employees in productive industries of enterprises 100 people, per capita annual output value 1 yuan. Now, X people need to be diverted from it to engage in service industry. Assuming that the average annual output value of those who continue to engage in productive industries after the diversion is 20% higher than the original, the average annual output value of those who engage in service industries after the diversion is 3.5a yuan. If we want to ensure that the total annual output value of the productive industries after the diversion is not less than half of that of the productive industries before the diversion, we should try our best to determine the number of people engaged in the service industry after the diversion.

16. Company A deals in two commodities, A and B. The purchase price of each commodity is120,000 yuan, and the price is145,000 yuan. The purchase price of each B commodity is 80,000 yuan, and the selling price is 654.38+10,000 yuan. Their purchase price and selling price remain unchanged. It is planned to purchase 20 pieces of Party A and 20 pieces of Party B, with the use capital of not less than 6.5438+0.92 million yuan and not more than 2 million yuan.

(1) What purchasing schemes does the company have?

(2) Which scheme can the company adopt to obtain the maximum profit? What is the maximum profit?

(3) If the profit obtained in (2) is used for re-purchasing, please directly prepare the purchasing plan to obtain the maximum profit.