$8\mathrm{.}5$ Economic Order Quantity $($EOQ$)$:

A distributor of small appliances wishes to calculate the optimal order quantity for replenishing its stock of a particular washing machine. Demand for the $$200$ machine is stable throughout the year and averages about $1000$ units annually. Each order involves the cost of transportation, receiving, and inspection, accounting for expenses of $$500$ per order. Holding costs are figured at $20\%$ per year.

a$.$ What order quantity minimizes the annual replenishment cost?

b$.$ How does the optimal cost break down into holding and carrying components?