Consider an $($M$,$L$)$ inventory system, in which the procurement quantity Q is defined by:

Q $=$ M $-1$ if I $<$ L

$0$ if I $>=$ L

Where I is the level of inventory on hand plus on order at the end of a month, M is the maximum inventory level, and L is the reorder point. M and L are under management control, so the pair $($M$,$ L$)$ is called the inventory policy. Under certain conditions, the analytical solution of such a model is possible, but not always. Use simulation to investigate an $($M$,$ L$)$ inventory system with the following properties: The inventory status is checked at the end of each month. Backordering is allowed at a cost of $$4$ per item short per month. When an order arrives, it will first be used to relieve the backorder. The lead time is given by a uniform distribution on the interval $[0\mathrm{.}25,1\mathrm{.}25]$ months. Let the beginning inventory level stand at $50$ units, with no orders outstanding. Let the holding cost be $$1$ per unit in inventory per month. Assume that the inventory position is reviewed each month. If an order is placed, its cost is $$60+$ $$5$Q$,$ where $$60$ is the ordering cost and $$5$ is the cost of each item. The time between demands is exponentially distributed with a mean of $1/15$ month. The size of demands follow this distribution: