*19. Aspiration Level Criterion. Acme Manufacturing uses an industrial chemical in one of its processes. The shelf life of the chemical is 1 month, following which any amount left is destroyed.

The use of the chemical by Acme (in gallons) occurs randomly according to the following distribution:

{20~, f(x) = ~, 100 :5 x :5 200 otherwise The actual consumption of the chemical occurs instantaneously at the start of the month. Acme wants to determine the level of the chemical that satisfies two conflicting criteria (or aspiration levels): The average excess quantity for the month does not exceed 20 gallons and the average shortage quantity for the month does not exceed 40 gallons.