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 $200$ gallons and a standard deviation of $100$ gallons. Goop sells the polymer for $$25$ per gallon. Goop purchases raw material for $$5$ per

gallon and must spend $$15$ 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 $13\mathrm{.}4.$

How many gallons should Goop purchase to maximize its expected profit? Use Table $13\mathrm{.}4.($Round your answer to $4$ decimal places. Enter

your answer a whole number.$)$

Answer: $!$

Suppose Goop purchases $100$ gallons of raw material. What is the probability that it will run out of raw material? $($Round your answer to $2$

decimal places.$)$

Answer:

Suppose Goop purchases $350$ gallons of raw material. What are the expected sales $($in gallons$)?$ Use Table $13\mathrm{.}4$ and the round$-$up rule. $($Round

your answer to $2$ decimal places.$)$

Answer:

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. $($Round your answer to $2$ decimal places.$)$

Answer: $

Suppose Goop wants to ensure that there is a $94$ 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. $($Enter your answer as a whole number.$)$

Answer: