$2^{nd}$ Inventory Management Problem $(3$ pts$)$

Emily Jones is the inventory control specialist for a company that manufactures high$-$end furniture. One of the company's top$-$selling items, a premium dining table, has an annual demand of $5,000$ units. The cost of each table is $$400,$ and the inventory carrying cost is $$25$ per table per year. The average ordering cost is $$45$ per order. An order takes about $3$ days to arrive, and the demand for one week is $100$ units. The company operates year$-$round with $280$ working days per year.

a$)$ What is the optimal number of days in between any two orders $($consider $250$ working day per year$)?$

b$)$ What is the annual cost of ordering and holding inventory?