2. (15 points) As mentioned in the text, before the Nissan plant in Smyrna, Tennessee, started to produce the Nissan Leaf they were imported from Japan. Although cars are now assembled in the US, some components still imported from Japan. Assume that the lead time from Japan is one weeks for shipping. Recall that the critical electrode material is imported from Japan. Each battery pack consists of 48 modules and each module contains four cells, for a total of 192 cells. Assume that each "unit" (the amount required for an individual cell in the battery pack) has a value of $3 and an associated carrying cost of 30%. Moreover, assume that Nissan is responsible for holding the inventory since the units are shipped from Japan. We suppose that placing an order costs $500. Assume that Nissan wants to provide a 99.9% service level for its assembly plant because any missing components will force the assembly lines to come to a halt. Use the 2020 demand observations to estimate the annual demand distribution assuming demand for Nissan Leafs is normally distributed. For simplicity, assume there are 360 days per year, 30 days per month, and 7 days per week. (a) What is the optimal order quantity? (b) What is the approximate time between orders? (c) What is the total annual inventory cost? (d) What is the reorder point with respect to the inventory position? Assume that the unit price can be decreased by 25 cents if at least 50,000 units will be ordered within a single order; and that can be reduced by 50 cents if at least 100,000 units are ordered. This price reduction applies to all the units being purchased in a single order. (e) What is the optimal order quantity? Please show all details of your calculation. Nissan LEAF The Nissan Leaf is a compact five-door hatchback electric car manufactured by Nissan and intro- duced in Japan and the United States in December 2010. The first vehicles sold in North America were produced at Nissan's plant in Oppama, Japan, which started production on October 22, 2010. Commercial U.S. production began in January 2013 at Nissan's manufacturing facility in Smyrna, Tennessee. The manufacturing plant was modified with a US$1.4 billion loan grant by the US De- partment of Energy to allow it to produce the Nissan Leaf and its advanced batteries. The Smyrna plant was originally expected to produce up to 150,000 vehicles and 200,000 battery packs per year. In Canada, the 2011 Nissan Leaf was priced at CA$38,395.00 and came with additional equip- ment useful for colder weather, such as heated front and rear seats, steering wheel, and outside mirrors. Other modifications included a battery heater system and an HVAC duct to the rear seating area. The initial roll-out was limited to selected markets and in limited quantities. Fleet deliveries in Canada began on July 29, 2011 and deliveries to individuals began in late September 2011. Additionally, Nissan produces all of its own battery packs. Since the beginning of 2013, the 24 kWh batteries that Nissan uses in all its vehicles have been produced at Nissan's new battery plant in Smyrna. Each battery pack consists of 48 modules and each module contains four cells, for a total of 192 cells. Nevertheless, the critical electrode material is still being shipped from Japan. In 2020, a total of 9559 Nissan Leafs were sold in the US. For the 12-month period starting January 2020 and ending December 2020, the detailed sales numbers are as follows: 626, 833, 489, 199, 410, 451, 662, 607, 637, 1576, 1270, and 1799 units.