① Open a shop to buy X TV sets, and then buy (100-x) washing machines.

According to the funds raised by the store,1800x+1500 * (100-x) ≤161800.

Simplify to get 300x≤ 1 1800, and solve to get x≤ 1 18/3.

X≥ (100-x) if the purchase quantity of TV sets is not less than half of that of washing machines.

Simplify to get 3/2*x≥50, and solve to get x≥ 100/3.

Because x must be an integer, ∴ x=34, 35, 36, 37, 38, 39.

Therefore, * * * has six purchase schemes. ① 34 TV sets and 66 washing machines; ② 35 TV sets and 65 washing machines; ③ 36 TV sets and 64 washing machines; ④ 37 TV sets and 63 washing machines; ⑤ 38 TV sets and 62 washing machines; ⑥ 39 TV sets and 6 1 washing machine.

② When selling TV sets and washing machines, the profit of TV sets is 2000- 1800=200 yuan, and the profit of washing machines is1600-1500 =100 yuan.

In order to get more profits, you should buy as many TV sets as possible for sale.

Therefore, when buying 39 TV sets and 6 1 washing machine, the store has the biggest profit. The maximum profit is 200 * 39+100 * 61=13900 yuan.

2,

(1) set car a x, and then car b (8-x).

According to the number of loquats, there are 4x+2(8-x)≥20. If you solve the inequality, you get x≥2.

According to the number of peaches, there are x+2(8-x)≥ 12. If the inequality is solved, x≤4 is obtained.

Therefore, * * * has three transportation schemes. (1) A car 2, B car 6; (2) There are 3 vehicles A and 5 vehicles B; (3) There are 4 vehicles for Car A and 4 vehicles for Car B..

(2) A car in 300 yuan, B car in 240 yuan.

In order to minimize the cost, you should use the B car as much as possible.

So when renting two cars A and six cars B, the freight is the least. Freight 300*2+240*6=2040 yuan.

3. When the water consumption is 5m? , the water fee is 1.5 * 5 = 7.5 < 15.

∴ Silver's water consumption exceeds 5 million? .

Let silver's water consumption xm? (x>5).

Then her water fee is 1.5*5+2(x-5)≥ 15.

Solve the inequality and get x≥8.75.

Therefore, when the water fee of Xiaoyinjia is not lower than 15 yuan, the water consumption is at least 8.75m? .

4, ∫| 3a-b+ 1 |≥0, |2a+3b-25|≥0, and | 3a-b+ 1 |+2a+3b-25 |≤ 0.

Then |3a-b+ 1|=0, |2a+3b-25|=0.

That is 3a-b=- 1, 2a+3b=25.

Solve the equation to get a=2 and b=7.

Then this set of inequalities is

4x-7 (x-7) > 19, simplified as -3x >-30, x < 10.

2 ÷ 2 * x+(3-7) x > 6, simplified as -3x > 6, x.

Therefore, the solution set of the inequality group is X.