Q$15\mathrm{.}1*($Teddy Bower$)$ Teddy Bower sources a parka from an Asian supplier for $$10$ each andsells them to customers for $$22$ each.Leftover parkas at the end of the season have nosalvage value. The demand forecast is normally distributed with mean $2,100$ and stan$-$dard deviation $1,200.$ Now suppose Teddy Bower found a reliable vendor in the UnitedStates that can produce parkas very quickly but at a higher price than Teddy Bower'sAsian supplier. Hence, in addition to parkas from Asia, Teddy Bower can buy an unlim$-$ited quantity of additional parkas from this American vendor at $$15$ each after demandis known.

a$.$ Suppose Teddy Bower orders $1,500$ parkas from the Asian supplier. What is the proba$-$bility that Teddy Bower will order from the American supplier once demand is known?$[15\mathrm{.}4]$

b$.$ Again assume that Teddy Bower orders $1,500$ parkas from the Asian supplier.Whatis the American supplier's expected demand; that is$,$ how many parkas should theAmerican supplier expect that Teddy Bower will order?$[15\mathrm{.}4]$

c$.$ Given the opportunity to order from the American supplier at $$15$ per parka, whatorder quantity from its Asian supplier now maximizes Teddy Bower's expectedprofit?$[15\mathrm{.}4]$

d$.$ Given the order quantity evaluated in part c$,$ what is Teddy Bower's expected profit?$[15\mathrm{.}4]$

e$.$ If Teddy Bower didn't order any parkas from the Asian supplier, then what wouldTeddy Bower's expected profit be$?[15\mathrm{.}4]$