Goop Incorporated 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 devation of $100$ gallons. Goop sells the polymer for $$26$ per gallon. Goop purchases raw materlal for $$9$ per gallon and must spend $$8$ per gallon to dispose of all unused raw materlal due to government regulations. $($One gallon of raw material ylelds 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 $13\mathrm{.}4.$

Note: If a part of the question specifles whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specifled method.

a$.$ How many gallons should Goop purchase to maximize its expected profit? Use Table $13\mathrm{.}4.$

Note: Enter your answer as a whole number.

Order quantity

b$.$ Suppose Goop purchases $120$ gallons of raw material. What is the probability that it will run out of raw material? Use Table $13\mathrm{.}4.$ Note: Round your answer to $4$ decimal places.

Probability

c$.$ Suppose Goop purchases $300$ gallons of raw material. What are the expected sales $($in gallons$)?$ Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Round your answer to $2$ decimal places.

Excepted sales

d$.$ Suppose Goop purchases $375$ gallons of raw material. How much should it expect to spend on disposal costs $($in dollars$)?$ Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Round your answer to $2$ decimal places.

Disposal cost

e$.$ Suppose Goop wants to ensure that there is a $91$ 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 $13\mathrm{.}4$ and the round$-$up rule.

Note: Enter your answer as a whole number.

Order quantity