1. Felgas, a manufacturer of felt gaskets, has production capacity of 1,000 units per day. Currently, the firm sells production capacity for $5 per unit. At this price, all production capacity gets booked about one week in advance. Some customers have said that they would be willing to pay twice as much ($10 per unit) if Felgas had capacity available on the last day. About 10 days in advance, demand for the high-price segment is normally distributed, with a mean of 250 and a standard deviation of 100. How much production capacity should Felgas reserve for the last day?

2. TheGoGo Bunny is a hot toy this Christmas, and the manufacturer has decided to ration supply to all retailers. A large retail chain owns two channelsa discount channel and a high-service channel. The retailer plans to sell the toy at a margin of $4 in the discount channel and a margin of $8 in the high-service channel. Any units sent to the discount channel are likely to sell out. The manufacturer sends 100,000 GoGo Bunnies to the retailer. The retailer has forecast that the demand for the toy at the high-service channel is normally distributed, with a mean of 400,000 and a standard deviation of 150,000. How many toys should the retailer send to the high-service channel?

3. A small warehouse has 100,000 square feet of capacity. The manager at the warehouse is in the process of signing contracts for storage space with customers. The contract has an upfront monthly fee of $200 per customer and then a fee of $3 per square foot based on actual usage. The warehouse guarantees the contracted amount even if it has to arrange for extra space at a price of $6 per square foot. The manager believes that customers are unlikely to use the full contracted amount at all times. Thus, he is thinking of signing contracts that exceed 100,000 square feet. He forecasts that unused space will be normally distributed, with a mean of 20,000 square feet and a standard deviation of 10,000 square feet. What is the total size of the contracts he should sign? If he forecasts that unused space will be normally distributed with a mean of 15 percent of the contracted amount and a coefficient of variation of 0.6, what is the total space that he should sign contracts for?

4. A trucking firm has a current capacity of 200,000 cubic feet. A large manufacturer is willing to purchase the entire capacity at $0.10 per cubic foot per day. The manager at the trucking firm has observed that on the spot market, trucking capacity sells for an average of $0.13 per cubic foot per day. Demand, however, is not guaranteed at this price. The manager forecasts daily demand on the spot market to be normally distributed, with a mean of 60,000 cubic feet and a standard deviation of 20,000. How much trucking capacity should the manager save for the spot market?

5. The manager at a large manufacturer is planning warehousing needs for the coming year. She predicts that warehousing needs will be normally distributed, with a mean of 500,000 square feet and a standard deviation of 150,000. The manager can obtain a full-year lease at $0.50 per square foot per month or purchase storage space on the spot market. Spot market rates have averaged $0.70 per square foot per month. How large an annual contract should the manager sign?