A factory has 360kg of raw material a and 290kg of raw material B. it produces 50 pieces of a and B with two kinds of raw materials It is known that 9kg of type a raw material and 3kg of type B raw material are needed to produce a product a; 4kg of type a raw material and 10kg of type B raw material are needed to produce a product B. what are the plans to produce a and B products according to the requirements

A factory has 360kg of raw material a and 290kg of raw material B. it produces 50 pieces of a and B with two kinds of raw materials It is known that 9kg of type a raw material and 3kg of type B raw material are needed to produce a product a; 4kg of type a raw material and 10kg of type B raw material are needed to produce a product B. what are the plans to produce a and B products according to the requirements

If x products a can be produced, then (50-x) products B can be produced
9x+4(50-x)

A factory has 360kg type a raw material and 290kg type B raw material. It plans to use these two raw materials to produce 50 pieces of products a and B. It is known that 9kg type a raw material and 3kg type B raw material are needed to produce one piece of product a; 4kg type a raw material and 10kg type B raw material are needed to produce one piece of product B
Q: there are several production schemes. Which one has the most profit?

Suppose we produce X pieces of product a and Y pieces of product B, then x + y = 50 and y = 50-x. according to the meaning of the title, there are 9x + 3Y ≤ 360, 3x + 10Y ≤ 290, that is, 9x + 3 (50-x) ≤ 360, 3x + 10 (50-x) ≤ 290, and the solution is x ≤ 35, X ≥ 30. Therefore, we can produce 30, 31, 32, 33, 34 or 35 pieces of product a and 35, 36, 37, 38, 39 or 40 pieces of product B. There are six schemes in total: 30 pieces of product a, 40 pieces of product B, 40 pieces of product B, 30 pieces of product a, 40 pieces of product B, 30 pieces of product a, 30 pieces of product B, There are 31 A products, 39 B products, 32 A products, 48 B products, 33 A products, 37 B products, 34 A products, 46 B products, 35 A products and 35 B products,

A factory has 360kg type a raw materials and 290kg type B raw materials. It plans to use these two raw materials to produce 50 pieces of products a and B. It is known that 9kg type a raw materials and 3kg type B raw materials are needed to produce a product a, 4kg type a raw materials and 10kg type B raw materials are needed to produce a product B. (1) suppose to produce X type a products, write out the inequality group that x should satisfy. (2) what kinds of production schemes are there? (3) If you can make a profit of 700 yuan for one a product and 1200 yuan for one B product, which production plan can make the total profit of a and B products the largest? What is the maximum profit?

(1) 9x + (50 − x) × 4 ≤ 3603x + (50 − x) × 10 ≤ 290; (2) solve the first inequality: X ≤ 32, solve the second inequality: X ≥ 30, ∵ 30 ≤ x ≤ 32, ∵ x is a positive integer, ∵ x = 30, 31, 32, 50-30 = 20, 50-31 = 19, 50-32 = 18, ∵ the production plan is: ① produce 30 pieces of product a, 20 pieces of product B; ② produce 31 pieces of product a, 19 pieces of product B; ③ produce 32 pieces of product a (3) total profit = 700 × x + 1200 × (50-x) = - 500X + 60000, ∵ - 500 ＜ 0, while 30 ≤ x ≤ 32, ∵ when x is smaller, the total profit is the largest, that is, when x = 30, the maximum profit is: - 500 × 30 + 60000 = 45000 yuan

A factory has 360 kg of type a raw materials and 290 kg of type B raw materials. It plans to use these two raw materials to produce 50 pieces of products a and B. It is known that one piece of product a will be produced
... the profit is 700 yuan when using 9kg of a raw material and 3kg of B raw material; the profit is 1200 yuan when using 4kg of a raw material and 10kg of B raw material to produce a B product. (1) to produce a and B products according to the requirements, find out the scheme; (2) suppose the total profit of producing a and B products is y yuan, and the number of one product is x, which scheme is the most profitable? What is the maximum profit?

Suppose we produce X pieces of product a and (50-x) pieces of product B. if we produce X pieces of product a with 9xkg of class a raw materials and 3xkg of class B raw materials, we can make a profit of 700X yuan. If we produce (50-x) pieces of product B with 4 (50-x) kg of class a raw materials and 10 (50-x) kg of class B raw materials, we can make a profit of 1200 yuan
(1) According to the meaning of the question, the system of inequalities can be listed
9x+4(50-x)≤360
3x+10(50-x)≤290
The solution set of inequality system is 30 ≤ x ≤ 32
The integer solution of inequality system is 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 qualified production schemes
Plan 1: produce 30 pieces of product a and 20 pieces of product B
Plan 2: 31 pieces of product a and 19 pieces of product B are produced
Plan 3: 32 products a and 18 products B are produced
(2) According to the meaning of the title, the total profit of producing two kinds of products is
y=700x+1200(50-x)
=700x+60000-1200x
=-500x+60000
When x is the minimum, y has the maximum, and the minimum of X is x = 30
When x = 30, y = - 500 × 30 + 60000 = 45000
A: scheme 1 is the most profitable, with a maximum profit of 45000 yuan