Problem set:

A plant uses $5000$ units per year of a certain subassembly that is purchased from a supplier at the price of $$600$ per unit. The plant operates $300$ days per year, and it uses a continuous review policy for the replenishment of this item, with an order size of $200$ units. Furthermore, the cost of placing and delivering an order is equal to $$300$ and the annual holding cost for this item is computed on the basis of an interest rate of $6\mathrm{.}0\%.$ Answer the following questions:

a$.$ What is the expected length of the replenishment cycles for this item? Please, state your answer in terms of working days.

b$.$ What is the resultant annual inventory holding plus ordering cost with respect to this item?