A warehouse purchases a certain component and supplies it to retailers. The warehouse operates $5$ days$/$week$,52$ weeks in a year. Only when it is open that the the orders can be received. The desired service level is $95\%.$ The following data are available$-$ The average daily demand $=100$ units Standard deviation of daily demand $=30$ units Lead time $=4$ days Inventory carrying cost $=$ Rs $11\mathrm{.}375/$unit$/$year Ordering Cost $=$ Rs $35/$order a$.$ What Order Quantity and ROP should be used? b$.$ If on$-$hand inventory is $40$ units, there is an open order for $400$ units and there is a Back$-$order for use of $30$ units, should a new order be placed? If yes, for how much quantity?