dolution

1.)

Aggregate production in the next four quarters is set to be 300 units in each quarter. Demand is 250, 250, 450, and 250 units respectively in each of the next four quarters. Beginning inventory is zero. If we are unable to meet the demand, it is not lost but backordered. Cost of holding one unit in inventory per quarter is $ 3, and the cost of having one unit of inventory backordered per quarter is $ 8. In the given production plan, what is the total cost of inventory (holding cost and backorder cost combined)? (For simplicity, assume that all shipments take place at the end of each quarter, not during the quarter)

2.) The beginning inventory is 30 units. The demand during the next four quarters are 72, 95, 77, and 53 units. The ending inventory should be 12 units. Using a level production plan, how many units should be produced each quarter? (Provide two digits to the right of the decimal point)

3.) The production during December was 80 units. Demand during the first four months in the next year is 100, 120, 110, and 80. Each unit increase of production (from one month to next) costs $200, and each unit drop costs $100 (for example, if January production was 85 units, a cost of 200*5 = $1000 is incurred; instead if January production was 78 units, a cost of 100*2 $200 is incurred). If a chase strategy is followed, what is the total cost of production increases and decreases in these four months? (The first change is from December to January; the last change is from March to April)