To find the total work done on the suitcase, we need to calculate the work done in lifting the suitcase up the stairs and the work done in pushing the suitcase horizonally.
The work done in lifting the suitcase up the stairs is equal to the force applied to lift the suitcase (200 N) multiplied by the distance it is lifted (10 m), or 200 N * 10 m = 2000 J.
The work done in pushing the suitcase horizontally is equal to the force appled to push the suitcase (50 N) multiplied by the distance it is pushed (35 m), or 50 N * 35 m = 1750 J.
The total work done on the suitcase is the sum of the work done in lifting it and the work done in pushing it, or 2000 J + 1750 J = 3750 J. Answer: \boxed{3750}.