A retailer orders custom tchotchkes from a specialty manufacturer. It costs the manufacturer $1 to make a tchotchke. The manufacturer sells the tchotchke to the retailer at $7. The retailer in turn will sell the tchotchke to customers at $20. If the tchotchke is not sold by the end of the season it is worthless and will have to be discarded. Assume that demand is normally distributed with a mean of 1000 and standard deviation of 200.

1. How many tchotchkes should the retailer order? What are the expected profits for the retailer and manufacturer? What is the total profit of the supply chain?
2. Now consider a scenario where the manufacturer will buy-back any unsold tchotchkes from the retailer at the end of the season for $3. How many tchotchkes should the retailer order? What are the expected profits for the retailer and manufacturer? What is the total profit of the supply chain?
3. Now consider a scenario where the manufacturer will sell tchotchkes to the retailer at cost ($1) but will take 53% of the sales revenue. How many tchotchkes should the retailer order? What are the expected profits for the retailer and manufacturer? What is the total profit of the supply chain?