JayHawks Fan Shop sells sports gears of KU. The shop sources KU basketball jersey from a Texas Supplier for $34 each and sells for $50 each. From previous years’ experience, the manager learned that the demand is uncertain at the time of orders placed. He then forecasts the demand of this particular type of jersey is normally distributed with mean 1,000 and standard deviation of 360. We assume the leftover jerseys at the end of the season have can be sold at outlet store for $10 each.
As descried in Problem 2, but now we suppose Jayhawks found a reliable vendor in Kansas that can produce this kind of jersey very quickly (you can assume lead-time for Kansas vendor is 0), but at a higher price than the Texas supplier. Hence, in addition to the Texas supplier, Jayhawks can source an unlimited quantity of additional jerseys from this Kansas vendor at $44 each after the demand is known.
Hint: Even though we have two suppliers here, the problem is still newsvendor.
(a) Suppose Jayhawks orders 1,400 jerseys from the Texas supplier. What is the probability that the manager of Jayhawks will order from the Kansas supplier once the demand is known?
(b) Assume that Jayhawks orders 1,400 jerseys from the Texas supplier. How many jerseys should the Kansas supplier expect Jayhawks to order from it?
(c) Given the opportunity to order from the Kansas supplier at $44 per jersey, what order quantity from its Texas supplier now maximizes Jayhawks’ expected profit?
(d) Given the order quantity in part (c) above, what is Jayhawks’ expected profit?
(e) If the manager of Jayhawks doesn’t order any jerseys from the Texas supplier, then what would Jayhawks’ expected profit be?