Mr. Dan Stockman is the procurement manager for Slicker Image (SI), an upscale retailer of novelty products. It is mid-August, and Mr. Stockman is wondering how many units of a new multi-function smart bracelet to order for the upcoming holiday season (November and December). The Malaysian manufacturer of this item, TechToys, requires orders to be placed in late August for delivery in late October, in time for holiday sales. Based on past experience with similar products, Mr. Stockman believes that the holiday demand (Nov-Dec) for the bracelet is Normally distributed with a mean of 3,000 units and standard deviation of 900. TechToys sells the item to SI at a unit price of $ 145 per unit, and SI has decided to set the retail price at $ 200 during the regular selling season (Nov-Dec). At the end of December, SI will mark down the price by 50% (i.e., sell the item for $ 100) to sell off any left-over items. TechToys incurs a cost of $ 105 per unit to manufacture this bracelet. For simplicity, ignore all supplier to SI (and vice versa) shipping costs. What order quantity would you suggest to maximize SIs expected profit? For your recommended ordering (and stocking quantity): i. What is SIs fill rate? ii. What is SIs expected profit offering the gadget during the upcoming season? iii. What is TechToys expected profit? iv. Briefly explain in managerial/intuitive terms why your recommended order quantity is higher or lower than Mr. Stockmans proposed order quantity of 4,000 units