Solution: (1) We assume that the quantity of these relief materials transported to D county is a ton, and the quantity transported to E county is b ton. ( 1)

Judging from the meaning of the question, {a+b=280a=2b-20(2 points).

The solution is {a= 180b= 100(3 points).

A: The quantity of this batch of relief materials delivered to County D is 180 tons, and the quantity delivered to County E is 100 tons. (4 points)

(2) According to the meaning of the question, get {120-x < 2xx-20 ≤ 25 (5 points).

The solution {x > 40x ≤ 45 means 40 < x ≤ 45.

∵x is an integer, and the value of ∴x is 4 1, 42, 43, 44, 45. (6 points)

There are five delivery schemes for this batch of relief materials.

The specific delivery scheme is:

Scheme 1: 4 1 ton of relief materials in Site A will be transported to County D and 59 tons to County E; 79 tons of relief materials in site B were transported to county D, and 2 1 ton was transported to county E..

Option 2: 42 tons of relief materials in place A are transported to county D and 58 tons to county E; 78 tons of relief materials in place B were transported to county D and 22 tons to county E..

Option 3: 43 tons of relief materials in place A are transported to county D and 57 tons to county E; 77 tons of relief materials from county B were transported to county D and 23 tons to county E..

Scheme 4: 44 tons of relief materials in place A are transported to county D and 56 tons to county E; 76 tons of relief materials from county B were transported to county D and 24 tons to county E..

Option 5: 45 tons of relief materials in Site A are transported to County D and 55 tons to County E; 75 tons of relief materials in place B are transported to county D and 25 tons to county E (7 points).

(3) Assume that the total cost of transporting this batch of relief materials is W yuan.

w = 220 x+250( 100-x)+200( 120-x)+220(x-20)+200×60+2 10×20 =-65438+。

Because w decreases with the increase of x, and 40 < x ≤ 45, x is an integer.

So when x=4 1, w has a maximum value. Then the total transportation cost of this batch of relief materials undertaken by the company is at most: w=60390 (RMB). (10)