FTX Inc, an electronics system integrator, is developing a new product as part of their annual generational upgrades. Owing to their long business history, they are considering Setronics as the supplier of hardware for this product. Setronics’ selling price is $103 per unit, including transportation costs. Due to long lead times and high setup costs, both firms agree on a single replenishment order before the upcoming annual season. Assume Setronics’ gross margin is 60% of its selling price for units produced in this pre-season order.
FTX’s recent annual demand forecast is Normally distributed with mean 11,452 and standard deviation 1700. FTX sells each unit, after integrating their proprietary software, for $197. Leftovers at the end of the season are liquidated for $30 per unit. FTX incurs holding costs at $1.7 per unit per month.
Make sure to use the following information in calculating Cu, Co, and holding costs when needed:
- FTX begins incurring holding costs upon delivery. Ignore holding costs at Setronics.
- "Leftover" items are held for the whole duration of the selling season.
- "Sold" items are held in the inventory for half the duration of the selling season (on average).
a) [45] How many of these units should FTX order to maximize their annual expected profits? Calculate resulting expected profits for FTX and Setronics. Hint: Use the Newsvendor model.