(10 points) 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 300 gallons and a standard deviation of 100 gallons. Goop sells the polymer for $28 per gallon. Goop purchases raw material for $13 per gallon and must spend $2 per gallon to dispose of 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 it has made and the rest of the demand is lost. Use Table 13.4. a. How many gallons should Goop purchase to maximize its expected profit? Use Table 13.4. (Round your answer to 4 decimal places. Enter your answer a whole number.) b. Suppose Goop purchases 170 gallons of raw material. What is the probability that it will run out of raw material? (Round your answer to 2 decimal places.) C. Suppose Goop purchases 350 gallons of raw material. What are the expected sales in gallons)? Use Table 13.4 and the round-up rule. (Round your answer to 2 decimal places.) d. Suppose Goop purchases 450 gallons of raw material. How much should it expect to spend on disposal costs (in dollars)? Use Table 3.14 and the round- up rule. (Round your answer to 2 decimal places.)