Goop Inc needs to order raw materials to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 200 gallons and a standard deviation of 100 gallons. Goop sells the polymer for $30 per gallon. Due to government regulations, goop purchases raw material for $10 per gallon and must spend $5 per gallon to dispose of all unused raw material. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what it made and the rest of the demand is lost.

Suppose Good purchases 250 gallons of raw material. What is the probability that they will run out of raw material?

Suppose Goop purchases 250 gallons of raw material. How many gallons of demand on average would remain unfulfilled?

Suppose Goop wants to ensure that there is a 90% probability that they will be able to satisfy the customers entire demand. How many gallons of raw material should they purchase?

Suppose Goop purchases 250 gallons of raw material. What would be its expected demand/supply mismatch cost?

How many gallons should Goop purchase to maximize its expected profit?