Samsung recently released a new version of its 65 inch OLED Smart TV. Due to the product's popularity, the availability maintained by Samsung and its main retailer, Amazon, has been extremely low. For example, Amazon.com had stock for one week early in February and then became stocked out for about 4 weeks; the product did not reappear on Amazon.com until March 9. Since these TVs are generally shipped from China by sea vessel, they also must clear U.S. customs before becoming available. The lead time for Amazon.com to replenish its stock (total time for shipping and customs) is 5 weeks.

i) Amazon.com sells the TV for $1500 online whereas it only costs them $900 to purchase the TV from Samsung. They anticipate that, at these prices, the mean of weekly demand is 40 TVs. When they order, they prefer to use a private container which costs roughly $3000 for shipping and can fit up to 500 TVs. Assuming Amazon's cost of capital is 30%, how many TVs should it order in each shipment?

ii) Given a lead time of 5 weeks, what inventory level should be the reorder point?

iii) On average, what is the ow time for a TV under the optimal inventory strategy (from when it arrives at Amazon.com until it is sold)?