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: Number of Items Demand during Month Received Month January 200 520 February 175 1,640 March 750 670 April 950 425 May 500 280 June 2,050 550 IE 3328/5331 Assume that starting inventory at the beginning of January is 480 units. Homework 4 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 case to make any sense.