You work as a clerk at a Bakery, a Malaysian bakery specialized in using tropical fruits in their pastries. Chris Peterson, the chef baker, wants to introduce a new pastry, durian cream puffs. Introducing this new pastry creates a new inventory problem for the bakery because durians have a strong smell and cannot be stored overnight in the fridge, lest they will ruin the taste of all the other food in the fridge. The durian cream would have to be ordered fresh daily.

Durian cream is purchased in pounds at RM 4.6 /lb (RM is the currency in Malaysia, and RM stands for Malaysian Ringgit). Chris predicts the demand will be 42 lbs of durian cream on average with a standard deviation of 3.36 lbs per day. You may assume that the demand is normally distributed. You estimate that each pound of durian cream will be sold at RM 12.88/lb.

How many pounds of durian cream should you order if you wish to maximize profitability?

What service level does your answer correspond to?

With your suggested order quantity from Part 1, how many pounds of durian cream can you expect to be short on a regular day?

What is the expected profit (in RM) with your suggested order quantity?