You need to complete the model and run a simulation of the inventory system for ONLY $10$ weeks. For this simulation you are to ALLOW FOR BACKORDERS $($this means you need to allow for a negative ending inventory$).$ If you have a negative ending inventory you will not have any carring cost but you will have a shortage cost. To compute the shortage cost multiple the number of units short by the per unit shortage cost of $$50.$ For instance if your ending inventory is $-3,$ the shortage cost would be $$150.$ The beginning inventory of the next period should also be negative if the previous period had a shortage. The leadtime for shipments is a constant $2$ weeks.

Answer the following questions for this $10$ week simulation:

Maximum Inventory during the $10$ weeks $\_\_\_\_\_\_\_\_$

Total number of orders in the $10$ weeks $\_\_\_\_\_\_\_\_$

Average weekly cost over the $10$ weeks $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Change the reorder point from $15$ to $20.$ What is the average weekly inventory cost now? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$