You are purchasing an exercise machine for a physical therapy office. the machine has a 20 inch vertical space where you add weights to increase the resistance for the patient. five pound weights are 3 inches high. two pound weights are 1 1/2 inches high. one pound weights are 1 inch. how much weight can the machine hold?

I would say 32 pounds.
here's why.
the most efficient weight in terms of size is the 5 pounder.
that 5 pounds / 3 inches = 1.67 pounds per inch.
the next most efficient weight in terms of size is the 2 pounder.
that's 2 pounds / 1.5 inches = 1.33 pounds per inch.
the least most efficient weight in terms of size is the 1 pounder.