It takes X days for Team A to complete it alone, Y days for Team A and Team B to complete it alone, and Z days for Team C to complete it alone. The following equation can be obtained: 6 (1/x+1/y) =1; 10( 1/Y+ 1/Z)= 1； 5( 1/x+ 1/z)= 2/3； X= 10，Y= 15，Z = 30

Another manufacturer gives team A a yuan and team B yuan every day; Pay C yuan to Team C, and you can get the equations: 6 (A+B) = 8700;

10(b+ C)= 9500； 5(A+C)= 5500； The solutions are A=800, B=650 and c = 300.

If the construction period does not exceed 15 days, it can only be completed by team A and team B, and team A needs XA=8000 yuan to complete it alone; Team a and team b need YB=9750 yuan to complete it alone. Therefore, it costs the least to finish it by team A alone.