1. Land’s End is deciding how many sunglasses to order from a small manufacturer. One option under consideration would have the manufacture sell the sunglasses to Land’s End for $65 and credit Land’s End $53 for each unit left unsold and returned at the end of the season. The cost to the manufacturer to produce the sunglasses is $25 per unit. Because styles change so much every year the returned sunglasses would have essentially no value. Land’s End will sell the sunglasses for $100 each.

Compute the cost of being understocked and overstocked for Land’s End. Then use those values to compute the critical ratio. The value of the critical ratio indicates that the expected profit maximizing in-stock probability for Land’s End is: a. 0.975 b. 0.7447 c. 0.66 d. 0.23533 e. 0.34

If Land’s End assumes that the demand for the sunglasses is normally distributed with mean of 200 and a standard deviation of 125, how many units should they purchase from manufacturer to maximize its (Land’s End) Expected profit?

If Land’s End order 400 pairs of sunglasses it could expect to have leftover inventory of 203 units. The manufacturer will buy back any leftovers at $53 each. Given that Land’s End orders 400 units what is the manufacture’s expected profit?

2. Teddy Bower purchases a fleece target for the cross country skiing market from an Asian supplier for $20 each. The fleece is sold to customer only in the United States at a price of $40 each. Any fleece leftover at the end of the season are discounted and sold for $15.00 each. The demand forecast for the fleece for the upcoming season in normally distributed with a mean of 20,000 and a standard deviation of 5,000.

What is the probability that the fleece will turn out to be a dog and only sell 12,000 or fewer units?

Assume that Teddy Bower orders 30,000 fleeces for the upcoming season. What is the probability that Teddy Bower will experience an out of stock condition?