A manufacturing company has been purchasing an item in lots of $600$ units. This equates to a

three$-$month supply. The cost per unit is $$16,$ the order cost is $$12$ per order, and the carrying

cost is $25\%$ of the value of the item. Assume that this company operates for $50$ weeks each year.

The lead time is $1$ week.

a$.(4$ points$)$ What is the optimal quantity order?

b$.(4$ points$)$ What is the number of weeks that elapse between two consecutive orders?

c$.(4$ points$)$ What is the number of orders placed per year?

d$.(4$ points$)$ What is the total cost of carrying inventory and placing orders?

e$.(4$ points$)$ Suppose that the company wants to keep a safety stock of $10$ items. What would

be the re$-$ordering point?