Consider an apparel supplier that is taking orders for dresses with a Christmas motif. The supplier's production capacity is for 5,000 dresses and each dress sold makes a margin of $10. The supplier is currently taking orders from retailers and must decide on how many orders to commit to at this time. At the time of delivery, if the supplier has orders that exceed capacity, it must arrange for backup capacity that results in a loss of $5 per dress.

a. Retailers have been known to cancel their orders near the winter season as they have better visibility into expected demand. How many orders should the supplier accept if cancellations are normally distributed with a mean of 800 and standard deviation of 400?

b. How will your answer change if the cancellations follow a Uniform distribution over [200, 1000]?