$3.)$ Sammy$$s wrenches is trying to create an inventory system for ordering it$$s #$10$ ratchet. They sell $250$ ratchets per week, with a standard deviation of $40($assume $52$ weeks per year$).$ Ratchets cost them $$\mathrm{.}40$ each. Ordering cost is $$40$ per order. The holding cost rate is $25\%.$ Lead time from their vendor is $2$ weeks. Please calculate the following:

a$.$ The EOQ amount for ratchets

b$.$ If Sammy wanted to maintain a $97\%$ service level, what ROP should be used?

c$.$ What is the total cost of the system you calculated above $($holding cost$,$ ordering cost and safety stock$).$

d$.$ If Sammy vendor$$s offered them a price discount to $$\mathrm{.}35$ each if they order in a bulk of $5,000$ units, should they take it$?$