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