LG Appliances produces home appliances, such as dishwashers, refrigerators, ovens etc. In your role as Operations Manager for LG Appliances, you have just completed forecasting the following demand for its refrigerators for the next 12 months: Month Demand January 3,900 February 4,030 March 4,900 April 7,230 May 8,500 June 7,230 July 6,590 August 8,210 September 12,500 October 11,200 November 7,900 December 5,950 Total 88,140 A worker can produce an average 220 refrigerators/month. Workers earn $4,300/month, and they do not work overtime. LG Appliances spends $1,800 for each employee it hires (with training), and it costs $3500 to lay off a worker. Hires and lay-offs occur on the first day of each month. At the end of each month, if there is any inventory on hand, it costs $40 per unit to carry to the next period. If there are unsatisfied orders (backorders) at the end of the month, a penalty cost of $100 per backordered unit is incurred. All backorders must be fulfilled by the end of December. There is currently no inventory available in stock at the beginning of January, and 30 employees are working in the company. Problem 2 The manager of LG Appliances realizes that the unsatisfied demand is lost to competitors. Hence, they need an aggregate plan that does not allow backorders. Using the information given in Problem 1, please answer the following questions: a) Prepare a level aggregate plan allowing inventories but not backorders. Display the amount of inventory at the end of each month. Calculate the total cost of this plan. b) The manager realizes an inventory record inaccuracy. It turns out that 1300 units of inventory were not seen in the company's information system, although it exists physically in the warehouse. Prepare a level aggregate plan with a starting inventory of 1300 units at the beginning of January. Again, inventories are allowed, but backorders are not. Your plan should display the amount of inventory at the end of each month. Compute the total cost of this plan.