To ensure a full line of outdoor clothing and accessories, the marketing department at Teddy Bower insists that they also sell waterproof hunting boots. Teddy Bower contacted several Taiwanese suppliers to request quotes. Due to competition, Teddy Bower knows that it cannot sell these boots for more than $54. However, $40 per boot was the best quote from the suppliers. In addition, Teddy Bower anticipates excess inventory will need to be sold off at a 50% discount at the end of the season. Given the $54 price, Teddy Bower’s demand forecast is normally distributed, with a mean of 400 boots and a standard deviation of 300.
If needed and possible, round to the nearest ten thousandth.
(1) Find Cu. (2) Find Co. (3) Compute the optimal service level. (4) Find the z-score that corresponds to the optimal service level. (5) Compute the optimal order quantity.