(1) Suppose that one type of x products are generated, and write the inequality group that the meaning of the problem x should satisfy; (2) According to the meaning of the question, what kinds of production schemes are there to arrange the number of production pieces of products A and B as required?
2. If a green vegetable produced in a certain place in our province is directly sold in the market, the profit per ton will be 1 1,000 yuan. After rough machining, the profit per ton can reach 4500 yuan. After finishing, the profit per ton rose to 7500 yuan.
A local agricultural and industrial company harvested 140 tons of this vegetable. The production capacity of the company's processing plants is as follows: If vegetables are imported,
Rough machining, machining16t; Every day; If finishing is carried out, 6 t can be processed every day, but the two processing methods cannot be carried out at the same time.
Limited by seasonal conditions, the company must sell or process all these vegetables within 15 days. Therefore, the company has formulated three feasible schemes:
Scheme 1: Roughly process all vegetables.
Option 2: Refine the vegetables as much as possible. Vegetables that are too late to be processed are sold directly in the market.
Scheme 3: It takes 15 days to sort out some vegetables and roughly process the rest.
Which scheme do you think is the most profitable? Why?
3. A car transports cement 12 tons at a time, and B car transports cement 10 tons at a time. If there are 720 tons of cement, please design several schemes to transport cement by table and explain the reasons.
Two people were invited to visit a scenic spot. There are three cars (with the same fare) going to the scenic spot at some time every day, but they don't know the comfort and the order of coming. They adopted different ride plans:
Anyway, A always gets on the bus first, and B observes before getting on the bus. When the first car came, he didn't get on the bus, but observed the comfort of the eclampsia car. If the second car is more comfortable than the first car, he will get on the second car. If the second car is not better than the first one, he will get on the third car.
If the comfort of these three cars is divided into three levels, please try to solve the following problems:
(1) What are the different possibilities for three cars to work in the order of appearance?
(2) Which scheme do you think A and B are more likely to take the bus? Why?
5. A factory has 360 kilograms of raw materials A and 290 kilograms of raw materials B, and plans 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 functional relationship between Y and X, and use the nature of the function to explain which production scheme has the largest total profit (1). What is the maximum profit?
6. A factory in Beijing and a factory in Shanghai made several computers at the same time. The factory in Beijing can support 10 foreign computers, and the factory in Shanghai can support 4 foreign computers. It is now decided to give Chongqing 8 sets and Hankou 6 sets. If the freight rates from Beijing to Hankou and Chongqing are 400 yuan/set and 800 yuan/set respectively, then the freight rates from Shanghai to Hankou and Chongqing are 300 yuan/set and 500 yuan/set respectively. Q:
(1) If the total freight is 8400 yuan, how many sets will be shipped from Shanghai to Hankou?
(2) How many transportation schemes does * * * have if the total freight is required to be less than 8200 yuan?
(3) Find out the transportation scheme with the lowest total freight. What is the lowest total freight?
7. The headmaster of a school will lead the city-level "three good students" of the school to travel to Beijing during the summer vacation. A travel agency said, "If the principal buys a full ticket, the rest of the students can enjoy a half-price discount." Travel agency B said: "All air tickets, including the principal, are 60% off the full fare." If the full fare is 240 yuan.
(1) Let the number of students be X, the charge of travel agency A be y A, and the charge of travel agency B be y B, and calculate the charges of the two travel agencies respectively (establish expressions);
(2) When the number of students is what, the fees charged by the two travel agencies are the same;
(3) Discuss which travel agency is more favorable in terms of the number of students.
8. One-time tickets sold in the park are 65,438 yuan each. At the same time, the ticketing method of purchasing "individual annual ticket" (the ticket holder can use it for one year from the date of purchase) is introduced. Annual tickets are divided into two categories: Class A annual tickets are each 100 yuan, and ticket holders do not need to buy tickets every time they enter the park. Each class B annual ticket is for 40 yuan, and the ticket holder needs to buy each ticket for 2 yuan every time he enters the park. At present, tourists A, B and C choose three ways to visit the park in a year, and each of them just enters the park X times a year.
Write out the annual admission expenses of B and C respectively (represented by an algebraic expression with X).
Among the annual ticket expenses of the three tourists, when A spends the least: ① How many times have B and C visited the park each in a year? ② Find the minimum of the total ticket fees paid by three tourists within one year.
9. A family decorated the kitchen with 480 tiles of the same specification from a certain brand. The tiles sold in the decoration materials shopping mall come in two kinds of packages, large and small, each with 50 pieces, and the price is 30 yuan; Small packages are 30 yuan each, and the price is 20 yuan. How can we make a purchase plan to minimize the cost if we don't unpack and retail all the packages?
10. It is known that Team A and Team B can complete a project in 12 days, and the project cost is 13800 yuan. The time for Team B to complete this project alone is twice as long as that for Team A, which is 10 days less, and the daily project cost of Team A is more than that of Team B 150.
(1) How many days will it take for Team A and Team B to finish this project alone?
(2) If the project management department decides to choose one of the two teams to complete the project alone, which project team should be chosen from the perspective of saving money? Please explain the reason.
I hope it works for you. Everything is fine. It's not that hard.