Solution: (1) If there are x middle-sized corners, there are (30-x) small corners. According to the meaning of the question, it is 80x+30 (30-x) ≤190050x+60 (30-x) ≤1620. When x= 19, 30-x =11; When x=20, 30-x = 10.

Therefore, there are three construction schemes: scheme 1, there are 18 medium-sized corners and 12 small corners; Scheme 2: medium corner 19, small corner11; Scheme 3: There are 20 middle-sized corners and 20 small corners 10.

(2) The cost of Scheme I is: 860×18+570×12 = 22,320 yuan;

The cost of the second scheme is: 860×19+570×11= 22610 (yuan);

The cost of the third scheme is: 860× 20+570×10 = 22,900 yuan.

Therefore, the first scheme has the lowest cost, with the lowest cost of 22,320 yuan.