Sarah has a craft shop that sells items online on Etsy. Once a year, in October,...

Sarah has a craft shop that sells items online on Etsy. Once a year, in October, she must plan for her special items sales for Valentine’s day. Her best seller for Valentine’s day is a heart-shaped keychain with the lovers’ names carved on it. Sarah does the carving right before shipping, but she must order all keychains from her supplier in October, to have them ready in January. She offers the keychain in her shop from January 15 to February 14. After February 14, people have no interest in buying the Valentine’s keychain anymore. The estimated demand during the selling period is normally distributed with a mean of 44 items and a standard deviation of 26 items considering that Sarah sells the keychains at $25 per unit and it costs her $5 per unit, please answer the following questions.

If Sarah decides to set the order quantity of Valentine’s day keychain to be 47:

Question 1

What would be the expected number of units short under this policy?

What would be the Item Fill Rate under this policy?

Question 2

Sarah has realized that her order quantity is not optimal and asks you to calculate the optimal value in order to maximize profit. How many keychains should Sarah order in October to maximize profit ?

Question 3

Sarah has hired a supply chain specialist to cross-check the order quantity that you have proposed. The supply chain specialist suggested to use an order quantity of 80. To show that your order quantity is truly the optimal value, you decided to calculate the expected profit for the order quantity that you proposed (in Question 2); and the expected profit for the order quantity recommended by the supply chain specialist.What is the expected profit using the order quantity that you proposed in Question 2?

What is the expected profit using the order quantity recommended by the supply chain specialist ?

Question 4

After doing some market research, Sarah discovers that she could sell the leftover inventory of keychains after Valentine’s day if the selling price is drastically reduced. She decides that she will be selling the remaining keychains after Valentine’s day at a discount price of $2 per unit. Considering this information, how many keychains should Sarah order in October to maximize profit ?

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