AQ$2.$ Inventory Management $(12$ marks$)$ A large dairy $$rm$,$ the Cow and Bu$$alo Company, buys bins every year, which it uses in the warehousing of its bottled products. A local vender has o$$ered the following discount schedule for bins: Order Quantity Unit Price $($$$)1$ to $399$ c $400$ to $7990$:$99$c $800$ to $1,4990$:$98$c $1,500$ or more $0$:$97$c The average yearly replacement is $3$; $600$ bins. The inventory carrying cost is $$12$ per bin per year and ordering cost per order is $$600.1.[9$ marks$]$ Determine the optimal order quantity for each order quantity range and the corresponding total cost. $2.[3$ marks$]$ Determine the range for c $($the unit price of the $$rst order quantity range$)$ such that EOQ is the optimal order quantity.