(Teddy Bower Boots) To ensure a full line of outdoor clothing and accessories, the marketing department at Teddy Bower insists that they also sell waterproof hunting boots. Unfortunately, neither Teddy Bower nor TeddySports has expertise in manufacturing those kinds of boots. Therefore, 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 sould off at a 50 percent discount at the end of the season. Given a $54 price, Teddy Bower's demand forecast is for 400 boots, with a standard deviation of 300.
a. If Teddy Bower decides to include these boots in its assortment, how many boots should it order from its supplier?
b. Suppose Teddy Bower orders 380 boots. What would its expected profit be?
c. John Briggs, a buyer in the procurement department, overheard at lunch a discussion of the "boot problem." He suggested that Teddy Bower ask for a quantity discount from the supplier. After following up on his suggestion, the supplier responded that Teddy Bower could get a 10 percent discount if they were willing to order at least 800 boots. If the objective is to maximize expected profit, how many boots should it order given this new offer?