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6. MR is a manufacturer of industrial fridges, freezers, and air conditioners. In December, the production planner needs to submit a production plan to the plant manager for the next year. The aggregate forecast for each quarter of next year is Q1: 14,800:02:26,400; Q3:35,000, and 04:19,200 units. The beginning inventory in January is 0, and the year-end inventory in December of next year can be 0. It costs MR $24 to hold an appliance in inventory for one quarter. Shortages are undesirable. Assume that all shortage will be back- ordered, and that back-order cost is $100 per unit per quarter. There are 160 permanent workers who produce 19,200 units per quarter. In busy quarters, workers can produce up to 9,600 additional units during overtime. Regular time labour cost is $60 per unit appliance and overtime labour cost is $83 per unit. MR can hire up to 160 temporary workers for a second shift. Assume temporary workers have the same productivity and can produce up to 19,200 units per quarter. A unit produced by temporary workers also costs $60 in labour cost. However, there will be an extra hiring cost of $25 per unit during the first quarter of employment. a. If permanent workers are used for the next four quarters during regular time, how many units will MR be short at the end of the year and in which quarters? b. Meet units short by hiring temporary workers. Use trade-off analysis to choose the minimum cost plan in this case. (Hint: Hire approximately 78 temps for two quarters starting in Q2.) c. Would using overtime (in addition to some temporary production) be less expensive? Use trade-off analysis to choose the overall minimum cost plan. (Hint: Hire approximately 38 temps for two quarters starting in Q2, supplemented with overtime.)