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 $200.00.The manufacturer sells a snowboard to SnowBirds for$100.00.SnowBirds will sell of all of the unsold snowboards for $50at the end of the selling season.SnowBirds estimates that demand for the snowboards during the season is normally distributed with a mean of 2,000and a standard deviation of 300.

Suppose SnowBirds wants to maximize expected profits from the sale of the snowboard.

a. What is the critical ratio Snowbirds would want to meet? (report your answer to 3 decimal places)

b. How many snowboards should they order from the manufacturer? (report your answer as an integer)

Suppose SnowBirds orders 2,400snowboards.

c. What are the expected lost sales? (report your answer to 2 decimal places)

d. What are the expected sales? (report your answer to 2 decimal places)

e. What is the expected leftover inventory? (report your answer to 2 decimal places)

f. What is the expected profit? (report your answer to 2 decimal places)

Suppose SnowBirds orders 1,900 snowboards.

g. What are the expected lost sales? (report your answer to 2 decimal places)

h. What are the expected sales? (report your answer to 2 decimal places)

i. How many of these snowboards can SnowBirds expect to sell at the discount price of $120. (report your answer to 2 decimal places)

j. How many snowboards should they order if they want to minimize their inventory while ensuring that the stockout probability is no greater than 3%? (report your answer as an integer)