Consider a Newsvendor model when the demand is normally distributed with a mean of $4,000$

and a standard deviation of $200.$ Also,

$\backslash$pi $=$ $$4/$unit

p $=$ $$3/$unit

c $=$ $$2/$unit

s $=$ $$1/$unit

$($a$)$ What is the optimal order quantity?

$($b$)$ Suppose now the standard deviation is changed to $100.$ What is the corresponding new

optimal order quantity?

$($c$)$ Explain the reason for the difference in your answers in $($a$)$ and $($b$)$ with a single sentence.