Q12.6** (Teddy Bower Parkas) Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 2,100 and standard deviation of 1,200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity.

a. Whatistheprobabilitythisparkaturnsouttobeadog,definedasaproductthatsells less than half of the forecast?

b. How many parkas should Teddy Bower buy from TeddySports to maximize expected profit?

c. IfTeddyBowerwishestoensurea98.5percentin-stockprobability,howmanyparkas should it order? For parts d and e, assume Teddy Bower orders 3,000 parkas.

d. Evaluate Teddy Bowers expected profit.

e. Evaluate Teddy Bowers stockout probability