This problem is to be worked out $$manually$$ i$.$e$.$ with a calculator

KraftyCity is a large retailer that sells power tools and other hardware supplies. One of its

products is the Krafty$-$Man workbench. Information on the workbench is as follows:

Annual Demand $=1200$

Holding cost $=$ $$15$ per unit per year.

Ordering cost $=$ $$200$ per order.

a$)$ What is the economic order quantity $($EOQ$)$ for the workbench? Show your calculation

clearly.

b$)$ Suppose that KraftyCity has to pay $$50$ per workbench for order under $200,$ but only $$42$

per workbench for orders $201$ or more. What order quantity should KraftyCity use?

Compute the total cost as $=[$ Holding cost $+$ Ordering Cost $+$ Material cost $]$ for the year

to arrive at your answer. Show your calculation clearly.

c$)$ The lead time for KraftyCity workbench is $3$ weeks, with a standard deviation of $1\mathrm{.}2$

weeks; and the average weekly demand is $24$ with a standard deviation of $8$

workbenches. What is the safety stock and reorder point, if KraftyCity wants to provide

a $95\%$ customer service level? Show your calculation clearly.

d$)$ Now suppose that the supplier of workbenches guarantees that the lead time will be a

constant $3$ weeks $($i$.$e$.$ standard deviation of lead time is now zero$).$ Recalculate the

safety stock and reorder point using the same service level of $95\%.$ Has the safety stock

level increased or decreased? Show your calculation clearly.