Okay, so:

But in this case F is not a constant.

Remember, F = ma = mg

But m is a function of the length of the cable here, so F is a function of the length of the cable as well.

What is the mass of the system in terms of the length of the cable?

mass = 1600 + 200*(10) - 10*(distance elevator has risen)

See how the mass decreases 10 lb for every foot the elevator has risen?

So then F = mg = (3600 - 10L)g, where L is the distance it has risen

Then we have:

And solve that bad boy. As a check, it should be less than if the mass stayed constant which would be 9.8*30*(3600) = 1058400