China Weizizhen Qiyuan

(1) Set up scenic spots and buy X long chairs and Y curved chairs.

Judging from the meaning of the title, 3x+5y =1300160x+200y = 56000,

X = 100y = 200。

A: I bought 100 long chairs and 200 curved chairs;

(2) If M Type A trucks are rented, 20 Type B trucks are rented.

4m+ 12(20？ m)≥ 100 1 1m+7(20？ m)≥200，

The solution is 15≤m≤ 17.5,

According to the meaning of the question, m is a positive integer,

So m can only be 15, 16, 17,

Therefore, there are three rental schemes for transporting these leisure chairs back at one time, which can be arranged as follows:

Scheme 1: type a 15, type b, 5,

Scheme 2: A-type trucks 16, B-type trucks 4,

Option 3: A-type trucks 17 and B-type trucks 3;

(3) If the total rent is W yuan, then W =1200m+1050 (20-m) =150m+21000.

∵ 150>0,

∴W increases with the increase of m,

∫ 15≤m≤ 17.5，

∴ When m= 15, W has a minimum value, and W is the minimum value =150×15+21000 = 23250.

The most economical car rental scheme is to rent 15 A truck and 5 B truck, and the minimum freight is 23250 yuan.