Please, explain your steps. I promise to like it $6.$ 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 Q$1$: $14,800$:$02$:$26,400$; Q$3$:$35,000,$ 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 Q$2.)$ 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 Q$2,$ supplemented with overtime.$)$