When 0≤x≤500, let the functional relationship be y=ax,
Then 500a=2800,
The solution is a=5.6,
Therefore, y=5.6x(0≤x≤500),
When x > 500, let the functional relationship be y=bx+c,
500b+c=2800 1000b+c=4800，
The solution is b=4 c=800.
Therefore, y = 4x+800 (x > 500),
To sum up, the functional relationship between y and x is y = 5.6x (0 ≤ x ≤ 500) 4x+800 (x > 500);
(2)y A =4× 1600+800=7200 (yuan),
Y b = 1600k，
When y a > y b, 7200 < 1600k,
That is, k > 4.5,
Therefore, when k > 4.5, it is more cost-effective for the park to choose B engineering team for construction.