SnowBirds is trying to decide on how many snowboards to purchase at the start of the upcoming selling season. A snowboard has a retail price of $350.00. The manufacturer sells a snowboard to SnowBirds for $200.00. SnowBirds will sell of all of the unsold snowboards for $150 at the end of the selling season. SnowBirds estimates that demand for the snowboards during the season is normally distributed with a mean of 3,000 and a standard deviation of 500.

a. [10 points] Suppose SnowBirds wants to maximize expected profits from the sale of the snowboard. How many snowboards should they order from the manufacturer? Report your answer as an integer.

b. [10 points] Suppose SnowBirds orders 3,800 snowboards. What is the expected profit? Report your answer to two decimal places.

c. [10 points] Suppose SnowBirds orders 3,400 snowboards. How many of these snowboards can SnowBirds expect to sell at the discount price of $120. Report your answer to two decimal places.

d. [10 points] How many snowboards should they order if they want to minimize their inventory while ensuring that the stockout probability is no greater than 4%? Report your answer as an integer.