The company has a monthly demand for a certain component of $6000$ units. The company's leader is considering a decision to procure this component in order to diversify the supply sources and reduce costs. The leader requests the procurement and production departments to compile relevant data for decision$-$making. The component is purchased at a price of $$35$ per unit. The cost of processing an order and placing it once is $$($X$+10).$ The annual warehouse rental fee is $$15$ per unit, the depreciation cost for equipment serving the warehouse is $Y per unit per year, and the interest rate is $9\%.$

Q$3.$ What is the optimal order quantity? What is the total inventory cost? $(1\mathrm{.}5$ points$)$

Q$4.$ How many orders should be placed? how long does it take between the orders? and reorder point if lead$-$time is X days?