i only need part D answered. please read through the question and not copy the same solution from other chegg questions. this one has different numbers

3. (5 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 $26 per gallon. Goop purchases raw material for $7 per gallon and must spend $12 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. a. How many gallons should Goop purchase to maximize its expected profit? (Use Table 13.4.) b. Suppose Goop purchases 150 gallons of raw material. What is the probability that it will run out of raw material? 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. d. Suppose Goop wants to ensure that there is a 90 percent probability that it will be able to satisfy its customers' entire demand. How many gallons of the raw material should it purchase? Use Table 13.4 and the round-up rule. Standard Normal Distribution Table