Acme Manufacturing uses a chemical in one of its processes. The shelf life is 1 month, and any amount left is destroyed. The amount, x, in gallons of the chemical used by Acme is represented by the following distribution:

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.

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f(x)= = 200 x² 0, 100 < x < 200 otherwise