Please solve using excel, and please provide all formulas. Thank you

Penalty costs can be assessed only against the number of units of demand that cannot be satisfied or against the number of units weighted by the amount of time that an order stays on the books. Consider the following history of supply and demand transactions for a particular part. Month January February March April May June Number of Items Received 200 175 750 950 500 2,050 Demand during Month 520 1,640 670 425 280 550 Assume that starting inventory at the beginning of January is 480 units. a. Determine the ending inventory each month. Assume that excess demands are back ordered. b. Assume that each time a unit is demanded that cannot be supplied immediately, a one-time charge of $10 is made. Determine the stock-out cost incurred during the six months (1) if excess demand at the end of each month is lost, and (2) if excess demand at the end of each month is back ordered. c. Suppose that each stock-out costs $10 per unit per month that the demand remains unfilled. If demands are filled on a first-come, first-served basis, what is the total stock- out cost incurred during the six months using this type of cost criterion? (Assume that the demand occurs at the beginning of the month for purposes of your calculation.) Notice that you must assume that excess demands are back ordered for this analysis to make any sense d. Discuss under what circumstances the cost criterion used in part (b) might be appropriate and under what circumstances the cost criterion used in part (c) might be appropriate