Skycell, a major European cell phone manufacturer, is making production plans for the last 8 months of the year. Skycell has worked with its customers (the service providers) to come up with forecasts of monthly requirements as shown in the spreadsheet named Question1. Assume that the demand during a stockout is backlogged and the cost of stocking out is $4 per phone per month. Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates for 20 days a month, 8 hours each day. One person can assemble a phone every 10 minutes. Workers are paid $20 per hour and a 50% premium for overtime. The plant currently employs 1,250 workers. Material costs for each cell phone total $20. Carrying inventory from one month to the next incurs a cost of $2 per phone per month. Assume that Skycell has a starting inventory of 50,000 units and wants to end the year with at least the same level of inventory, 50,000 units. a) Assuming no subcontracting, no new hires, no layoffs, and no maximum overtime limit (overtime is allowed), what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan? b) Assume that a third party has offered to produce cell phones as needed at a cost of $25 per unit (this includes component costs of $20 per unit). Also, Skycell can now hire and lay off employees. The cost of hiring them is $1,250 per employee and the layoff cost is $1,750 per employee. Overtime is limited to at most 20 hours per employee per month. Assume that all the demand during a stockout is backlogged and the firm plans to meet all of the demand. For this case, what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan? Also report the average amount of time that a product spends in the system, from production to sales (in months). c) For the case provided in part (b), consider the scenario in which Skycell aims for a level production schedule. For this case, what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan? d) For the case provided in part (b), consider the scenario in which all the demand during a stockout is lost and the cost of stocking out is $24.5 per phone. For this case, what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan? Also report the average amount of time that a product spends in the system, from production to sales (in months).