Geoff Gullo owns a small firm that manufactures "Gullo Sunglasses." He has the opportunity to sell a particular seasonal model to the retailer Land's...

Geoff Gullo owns a small firm that manufactures "Gullo Sunglasses." He has the opportunity to sell a particular seasonal model to the retailer Land's End. This season's demand for this model will be normally distributed with a mean of 200 and a standard deviation of 80. Land's End will sell those sunglasses for $100 each and can dispose the unsold sunglasses at the end of the seasons free of charge.

a)    Currently Geoff offers a price of $30 for each unit of sunglasses to Land's End. How many units Land's End would buy from Geoff and what is Land's End's expected profit?

b)   Geoff considers a different purchasing option for Land's End. In particular, Geoff agrees to let Land's End first reserve the sunglasses before the season starts for a reservation price of $24. Land's End then can ask for the delivery of sunglasses within the reserved capacity for an exercise price of $6 for each unit after the season's demand is realized. How much Land's End would buy from Geoff and what is Land's End's expected profit?

c)    If we compare the purchasing option in a) and purchasing option in b)

                       i.        Which purchasing option should Land's End choose? Why is Land's End profit higher in that option (compared to the other option)? Is this option also preferred by Geoff Gullo (please assume that unit production cost of Geoff Gullo is normalized to zero)? Why (not)? In calculating Geoff Gullo's expected profit please consider how much Land's End reserves first and then how much Land's End exercises later.

                     ii.        As demand variability increases (let's say from standard deviation of 80 to 90 then to 100), how is the difference between Land's End's profit with purchasing option in b) and Land's End's profit purchasing option a) affected? Please explain why you observe such a pattern qualitatively.