Weekly Demand, Occurrence week

$95,8$

$96,2$

$97,6$

$98,10$

$99,8$

$100,6$

$101,6$

$102,2$

$103,4$

Total $,52$ Question $1$

Bold Bodybuilders, Inc. is a large sporting goods store. It has become the exclusive distributor of the new body building equipment called Geni. After carrying the equipment for a year, Joe Sabatini, a manager of supply chain, decided to analyze the company's inventory policy for Geni. On the basis of the past year's record, Joe has identified the following weekly demand data:

The annual demand for Geni is considered to be $5,128$ units, annual holding cost per equipment is $$244,$ and ordering cost is $$4,250$ per order. The equipment price is $$929$ per unit. The new order is made when the inventory level in the store drops to a predetermined number of units on hand. Once the company orders Geni from the supplier, it will come to the store in about $3$ weeks.

Questions $($Please fill in your answer using the enclosed Excel answer template$)$

a$)$ Explain briefly on how to calculate the mean and the standard deviation of weekly demand.

b$)$ What are the expected demand during lead time? What is the standard deviation of the demand during the lead time? Please explain your calculation briefly.

c$)$ What are the safety stock and reorder point that may guarantee with a probability of $97\%$ that the store will not run out of stock of Geni equipment $(97\%$ service level$)$ during the reordering. Explain how you reach the result.