To ensure a full line of outdoor clothing and accessories, the marketing depaliment at Teddy Bower insists that they also sell waterproof hunting boots. Unfortunately, neither Teddy Bower nor Teddy Sports 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 sold off at a 50 percent discount at the end of the season. Given the $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 fill rate be?

c. Suppose Teddy Bower orders 3 80 boots. What would its expected profit be?

d. The marketing department will not be happy with the planned order quantity (from part a). They are likely to argue that Teddy Bower is a service-oriented company that requires a high fill rate. In particular, they insist that Teddy Bower order enough boots to have at least a 98 percent fill rate. What order quantity yields a 98 percent fill rate for Teddy Bower?

e. What would Teddy Bower's expected profit be with the order quantity from part d?

f. 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?

g. After getting involved with the "boot problem," John Briggs became curious about using AIF ratios to forecast. He directed his curiosity to another product, Teddy Bower's standard hunting boot, which has a demand forecast for 1 ,000 units. This boot sells for $55, and because of Teddy Bower's volume, the supplier of this boot only charges $30. The standard hunting boot never goes out of style (therefore, all leftover boots will be sold next year, but it is a seasonal product). It costs Teddy Bower $2.50 to hold a boot over from one season to the season in the following year. Furthermore, Teddy Bower anticipates that the selling price and procurement cost of this boot will be the same next year (i.e., $55 and $30, respectively). He collected the following data on 20 items that he felt were similar in nature to hunting boots. Using these data collected by John Briggs, what is Teddy Bower's profit-maximizing order quantity?