Need assistance with setting up the problems below.
JayHawks Fan Shop sells sports gears of KU. The shop sources a basketball jersey from a Texas Supplier for $10 each and sells for $25 each. We already learned that the demand is uncertain at the time of orders placed. The manager forecasts the demand of this kind of jersey is normally distributed with mean 2,000 and standard deviation of 500. We assume the leftover jerseys at the end of the season have no salvage value.
Now, we suppose Jayhawks found a reliable vendor in Kansas that can produce this kind of jersey very quickly (much shorter lead time) but at a higher price than the Texas supplier. Hence, in addition to the Texas supplier, Jayhawks can buy an unlimited quantity of additional jerseys from this Kansas vendor at $15 each after the demand is known. Suppose after the demand is known, ordering from the Texas supplier is not possible because of the long lead time.
(a) Suppose Jayhawks orders 2,500 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? [4 pts]
(b) Assume that Jayhawks orders 2,200 jerseys from the Texas supplier. How many jerseys should the Kansas supplier expect Jayhawks to order from it? [5 pts]
(c) Given the opportunity to order from the Kansas supplier at $15 per jersey, what order quantity from its Texas supplier now maximizes Jayhawks’ expected profit? (Hint: Even though we have two suppliers here, the problem is still a newsvendor. Carefully think how underage and overage costs are affected by the presence of the Kansas supplier, i.e., 2nd order opportunity