Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer 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's 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. (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 Goop purchases 150 gallons of raw material. What is the probability that they will run out of raw material?

Suppose Goop purchases 300 gallons of raw material. How many gallons of demand on average would remain unfulfilled?

Suppose Goop purchases 400 gallons of raw material. How much should they expect to spend on disposal costs (in $s)?

Now, Suppose Goop purchases 425 gallons of raw material. How many gallons of demand on average would remain unfulfilled?

Can you explain why the probability of stockout and (un)Fill Rate in 2.5 and 2.6 might be different?