1. 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 9 kilograms of raw materials A and 3 kilograms of raw materials B are needed to produce a product A, and 4 kilograms of raw materials A and 65,438+00 kilograms of raw materials B are needed to produce a product B. Please design the production plan of products A and B as required.

Solution:

Assuming that X products A and Y products B are produced, the equation is obtained:

9x+4y=360

3x+ 10y=290

Solve the above equation and get

y = 255/ 13 = 19+8/ 13，

Take y= 19, because 50 pieces of A and B products will be produced, then x=3 1.

Substitute x=3 1 into the upper equations.

9*3 1+4* 19=355 is less than 360, and 360-355=6.

3 * 31+10 *19 = 283 less than 290, 290-283 = 7.

A: We have produced 365,438+0 A products and 65,438+09 B products. There are 6 kilograms of raw material A and 7 kilograms of material B. ..

2. Solution: The mall is planned to invest X yuan, with a profit of * * * at the beginning of the month 1 yuan and a profit of y2 yuan at the end of the month.

y 1 = 15% x+(x+ 15% x) 10% = 0.265 x，

y2=30%x-700=0.3x-700。

∴y 1-y2=0.265x-(0.3x-700)=700-0.035x.

① When y 1-y2=0, there are 700-0.035x=0, ∴x=20000.

When x=20000, the profits of the two sales methods are the same.

② when y 1-y2>0-y2 > 0, there are 700-0.035x > 0, ∴ x < 20000.

When x < 20000, y 1 > y2. That is, the sales at the beginning of the month are more profitable.

③ When y 1-y2 20000.

∴ when x > 20000, y 1 < y2. In other words, the sales at the end of the month are more profitable.