1. The GOGO bunny is a hot toy this Christmas, and the manufacturer has decided to ration supply to all retailers. A large retail chain owns two channels- a 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. The manufacturer sends 100,000 GoGo bunnies to the retailer. The retailer has forecast that the demand for the toy is 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?

2. 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 $0.13 per cubic foot per day. Demand however is not guaranteed at this price. The manager forecast 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?

3. A department store has purchased 5,000 swimsuits to be sold during the summer sales season. The season lasts three months and the store manager forecasts that customers buying early in the season are likely to be less price sensitive and those buying later in the season are likely to be more price sensitive. The demand curves in each of the three months are forecast to be as follows: d1 = 2,000 - 10p1, d2 = 2,000 - 20p2, and d3 = 2,000 - 30p3. If the department store is to charge a fixed price over the entire season, what should it be? What is the resulting revenue? If the department store wants dynamic prices that vary by month, what should they be? How does this affect profits relative to charging fixed prices?