Teddy Bower sources a parka from an Asian supplier for $10 each and sells them to customers for $22 each. Leftover parkas at the end of the season have no salvage value. (Recall Q12.6.) The demand forecast is normally distributed with mean 2,100 and standard deviation 1,200. Now suppose Teddy Bower found a reliable vendor in the United States that can produce parkas very quickly but at a higher price than Teddy Bower's Asian supplier.
Hence, in addition to parkas from Asia, Teddy Bower can buy an unlimited quantity of additional parkas from this American vendor at $15 each after demand is known.
a. Suppose Teddy Bower orders 1,500 parkas from the Asian supplier. What is the probability that Teddy Bower will order from the American supplier once demand is known?
b. Again assume that Teddy Bower orders 1,500 parkas from the Asian supplier. What is the American supplier's expected demand; that is, how many parkas should the American supplier expect that Teddy Bower will order?
c. Given the opportunity to order from the American supplier at $15 per parka, what order quantity from its Asian supplier now maximizes Teddy Bower's expected profit?
d. Given the order quantity evaluated in part c, what is Teddy Bower's expected profit?
e. If Teddy Bower didn't order any parkas from the Asian supplier, then what would Teddy Bower's expected profit be?