A factory has 226kg of Class A raw materials

Solution: (1) According to the problem, we get {7x+3(40-x) 2264x+10(40-x) 250, and the solution set of this inequality group is 25 x

x is an integer, so x = 25 or 26

Therefore, there are two production schemes that meet the theme:

25 A products and 15 B products were produced;

It produced 26 A products and 14 B products

2) The material price of a product A is: 7 50 + 4 40 = 510 yuan The material price of a product B is: 3 50 + 10 40 = 550 yuan The total price of the program is:

25 510 + 15 550 yuan The total price of the plan is: 26 510 + 14 550 yuan 25 510 + 15 550-(26 510 + 14 550) = 550-510 = 40 yuan

It can be seen from this that the total price of the plan is less than the total price of the plan, so the plan is better

Test Topic: Application of Unary Inequality Groups Topic: Scheme-based; Graphical Analysis:

1) The inequality relationship in this problem is: raw material A used in the production of product A + raw material A used in the production of product B 226, raw material B used in the production of product A + raw material B used in the production of product B 250, from which the inequality group can be obtained, the value range of the independent variable is obtained, and then the value of the independent variable that meets the requirements is obtained according to the value range of the independent variable

2) According to the production plan obtained from (1), then calculate how much it costs to produce products A and B respectively, compare them, and judge the most money-saving plan Answer: Solution: (1) If the production of product A is x, then product B (40-x) pieces, according to the topic, 7x+3(40-x) 2264x+10(40-x) 250, and the solution set of this inequality group is 25 x

x is an integer, so x = 25 or 26

Therefore, there are two production schemes that meet the theme:

25 A products and 15 B products were produced;

It produced 26 A products and 14 B products

2) The material price of a product A is: 7 50 + 4 40 = 510 yuan

The material price of a B product is: 3 50 + 10 40 = 550 yuan

The total price of the plan is: 25 510 + 15 550 yuan

The total price of the plan is: 26 510 + 14 550 yuan

25 510 + 15 550 - (26 510 + 14 550) = 550-510 = 40 yuan

It can be seen from this that the total price of the scheme is less than the total price of the scheme, so the scheme is better Comments: This question examines the application of the unary inequality group, connects real-life events with mathematical ideas, and understands the meaning of the question, 1) According to the "raw material A used in the production of product A + raw material A used in the production of product B 226, raw material B used in the production of product A + raw material B used in the production of product B 250" can be solved

2) first calculate the material price of a product A and the material price of a product B, and then calculate it according to the plan

Let A be x pieces, then B is 40 x pieces.

There are two schemes: 7x 3 (40 x) 226 and 4x 10 (40 x) 250

From equation 1: x, that is, 26 whole pieces, 224kg of A, 244kg of B;

From Equation 2: x 25, A needs 226kg, B 250kg;

That is, the solution of A26 pieces and B14 pieces is good, because the task is completed and the raw materials are saved, and the cost will be low.

Solution: (1) If the production of product A X pieces, then B product (40-X) pieces, according to the theme, obtain.

The solution set for the group of inequalities 7x+3(40-x) 2264x+10(40-x) 250 is 25 x

x is an integer, so x = 25 or 26

Therefore, there are two production schemes that meet the theme:

25 A products and 15 B products were produced;

It produced 26 A products and 14 B products

2) The material price of a product A is: 7 50 + 4 40 = 510 yuan The material price of a product B is: 3 50 + 10 40 = 550 yuan The total price of the program is:

25 510 + 15 550 yuan The total price of the plan is: 26 510 + 14 550 yuan 25 510 + 15 550-(26 510 + 14 550) = 550-510 = 40 yuan

It can be seen from this that the total price of the plan is less than the total price of the plan, so the plan is better

Solution: Set up the production of X pieces of A products and 50-X pieces of B products; The production of X pieces of A products requires 9x kg of A raw materials and 3x kg of B raw materials, and a profit of 700x yuan can be obtained; The production of (50-x) pieces of B products requires 4 (50-x) kg of raw materials of type A and 10 (50-x) kg of raw materials of type B, and a profit of 1200 (50-x) yuan can be obtained.

): According to the title, the inequality group can be listed:

9x+4(50-x)≤360 ①

3x+10(50-x)≤290 ②

Solve the inequality 9x+200-4x 360

9x-4x≤360-200

5x≤160

x 32 solution inequality

3x+500-10x≤290

3x-10x≤290-500

7x≤-210

The solution set for a group of x30 inequalities is 30 x 32, and the integer solutions for groups of inequalities are x=30, x=31, x=32

When x=30, 50-x=20

When x=31, 50-x=19

When x=32, 50-x=18

There are three production options:

Plan 1: Production of 30 products of A, 20 of products of B, Plan 2: Production of 31 products of A, 19 of products of B, Plan 3:

There are 32 products in production A and 18 products in B ( ) y = 700x + 1200 (50-x) = 700x + 60000-1200x

500x+60000

The function y=-500x+60000, y decreases with the increase of x, and the value of x is 30 x 32

When x=30, y has a maximum value, y=-500 30+60000=45000 ( ) in the scheme 1 profit is the largest, the maximum profit is 45000 yuan.

1) If the production of product A X pieces, the production of product B (50-X) pieces is extremely large.

However, the raw materials do not necessarily need to be used up, so the following two inequalities can be established:

9x+4(50-x)≤355

3x+10(50-x)≤310

The solution is: 190 7 x 31, and since x is an integer, the value of x can be .

That is, there are the following four schemes:1 a28 b22；2. a29 b21；3. a30 b20；4. a31 b19。

2) From the inscription, it can be seen that the production number of product A is x, and the production number of product B is (50-x).

So y=900x+1100(50-x)=55000-200x.

From this functional relation, it can be seen that the less product A produces, the better, so (1) the production of 28 pieces of product A, 22 pieces of product B can obtain the largest total profit, which is 55000-200 * 28 = 49400 yuan.

Solution: If x pieces of A products are produced, then (50-x) B products are produced 9x+4 (50-x) 360··· 13x+10(50-x) 290··· 2 out of 1: 9x+200-4x 360

5x≤160

x 32 is obtained by 2: 3x+500-10x 290

500-7x≤290

7x≥210

x 30 Because x is an integer, x=30,31,32

So there are three schemes: 1: 30 pieces of A products, 20 pieces of B products, 2: 31 pieces of A products, and 19 pieces of B products.

3: 32 products of A and 18 of B products.

y=700x+1200（50-x）

500x+60000

When x=30, the minimum value of y is -500 30+60000=45000 I also did it here, I hope it can help you

Solution (1): If a factory is set up to produce X tons of product A, it is necessary to produce B product (8-X) tons; The profit obtained from the production of X tons of A products is 10,000 yuan, and the profit obtained from the production of (8-X) tons of B products is 10,000 yuan; According to the title, the total profit is: y==

y=Because x 0 and 8-x 0, the range of x is 0 x 8(2): if a factory is set up to produce x tons of product A, it will produce (8-x) tons of product B; The production of X tons of A products requires tons of raw materials of A and tons of raw materials of B; The production of (8-x) tons of B products requires tons of raw materials from A and tons of raw materials from B; Depending on the title, there are groups of inequalities:

Solve inequality (1) to get: x

Solve inequality (2) to get: x

So, the solution of the group of inequalities is.

Because the total profit y= , when x takes the minimum value, y has a maximum value and when x=, the maximum profit y=

Therefore, when a chemical plant produces tons of product A, the maximum profit obtained is 10,000 yuan.

If product A has x pieces, then product B is 50-x pieces.

9x+4(50-x)<=360 is reduced to x<=323x+10(50-x)<=290, reduced to x>=30x, it must be an integer, so there are 3 values of Yuyan

When there are 30 pieces for product A, there are 20 pieces for product B.

When there are 31 pieces of product A, there are 19 pieces of product B.

When there are 32 pieces of product A and 18 pieces of product B. Three scenarios.

Let the quantity of A be x, the total profit be y, and the quantity of B is 50-x pieces.

y = 700x + 1200 (50-x) simplified to y = 60000-500x It can be seen that when the value of x is smaller, the value of y is larger, and the minimum value is 30, then when the number of a is 30, the number of b is 20, the profit is the largest, and the profit is 60000-500 30 = 45000 yuan.

Set up the production of product A x pieces, B product Y pieces, then.

x+y=50

9x+4y≤360

3x+10y≤290

Solution: 30 x 32

Then the scheme and profit are as follows:

Production of 30 pieces of product A, 20 pieces of product B, profit: 45,000 yuan to produce 31 pieces of product A, 19 pieces of product B, profit: 43,500 yuan to produce 32 pieces of product A, 18 pieces of product B, profit:

44,000 yuan, so the production of 30 pieces of product A, 20 pieces of product B, the most profitable.

Solution: (1) According to the problem, we get {7x+3(40-x) 2264x+10(40-x) 250, and the solution set of this inequality group is 25 x

x is an integer, so x = 25 or 26

Therefore, there are two production schemes that meet the theme:

25 A products and 15 B products were produced;

It produced 26 A products and 14 B products

2) The material price of a product A is: 7 50 + 4 40 = 510 yuan The material price of a product B is: 3 50 + 10 40 = 550 yuan The total price of the program is:

25 510 + 15 550 yuan The total price of the plan is: 26 510 + 14 550 yuan 25 510 + 15 550-(26 510 + 14 550) = 550-510 = 40 yuan

It can be seen from this that the total price of the plan is less than the total price of the plan, so the plan is better

Test Topic: Application of Unary Inequality Groups Topic: Scheme-based; Graphical Analysis:

1) The inequality relationship in this problem is: raw material A used in the production of product A + raw material A used in the production of product B 226, raw material B used in the production of product A + raw material B used in the production of product B 250, from which the inequality group can be obtained, the value range of the independent variable is obtained, and then the value of the independent variable that meets the requirements is obtained according to the value range of the independent variable

2) According to the production plan obtained from (1), then calculate how much it costs to produce products A and B respectively, compare them, and judge the most money-saving plan Answer: Solution: (1) If the production of product A is x, then product B (40-x) pieces, according to the topic, 7x+3(40-x) 2264x+10(40-x) 250, and the solution set of this inequality group is 25 x

x is an integer, so x = 25 or 26

Therefore, there are two production schemes that meet the theme:

25 A products and 15 B products were produced;

It produced 26 A products and 14 B products

2) The material price of a product A is: 7 50 + 4 40 = 510 yuan

The material price of a B product is: 3 50 + 10 40 = 550 yuan

The total price of the plan is: 25 510 + 15 550 yuan

The total price of the plan is: 26 510 + 14 550 yuan

25 510 + 15 550 - (26 510 + 14 550) = 550-510 = 40 yuan

It can be seen from this that the total price of the scheme is less than the total price of the scheme, so the scheme is better Comments: This question examines the application of the unary inequality group, connects real-life events with mathematical ideas, and understands the meaning of the question, 1) According to the "raw material A used in the production of product A + raw material A used in the production of product B 226, raw material B used in the production of product A + raw material B used in the production of product B 250" can be solved

2) first calculate the material price of a product A and the material price of a product B, and then calculate it according to the plan