PA $13-5($Algo$)$ Teddy Bower is an outdoor clothing and accessories chain...

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $$8$ each from its Asian supplier,

TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that its demand is

normally distributed with a mean of $1,900$ and a standard deviation of $1,500.$ Teddy Bower sells these parkas at $$23$ each. Unsold

barkas have little salvage value; Teddy Bower simply gives them away to a charity $($and also doesn't collect a tax benefit for the

donation$).$ Use Table $13\mathrm{.}4.$

Note: Do not round intermediate calculations. If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then

Eredit for a correct answer will depend on using the specified method.

a$.$ How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Enter your answer as a whole number.

Order quantity

$2,478$

b$.$ If Teddy Bower orders $3,500$ parkas, what is expected leftover inventory? Use Table $13\mathrm{.}4$ and the round$-$up rule.

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

Expected leftover inventory

c$.$ If Teddy Bower orders $3,500$ parkas, what is expected sales? Use your result from Part b$.$Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $$8$ each from its Asian supplier, TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with a mean of $1,900$ and a standard deviation of $1,500.$ Teddy Bower sells these parkas at $$23$ each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity $($and also doesn$$t collect a tax benefit for the donation$).$ Use Table $13\mathrm{.}4.$

Note: Do not round intermediate calculations. If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specified method.