Question: Goop Inc. needs to order a raw material to make a special polymer. (Assume that one gallon of raw material yields one gallon of polymer.)

Goop Inc. needs to order a raw material to make a special polymer. (Assume that one gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost.

Suppose the demand for the polymer (for the upcoming selling season) is forecasted to be normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose-off all unused raw material due to government regulations. How many gallons should Goop purchase to maximize its expected profit?

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