$($PLEASE SOLVE HANDWRITING WITHOUT EXCEL$)$Inventory Management $-$ Part $2)$ An electrical repair firm inventories three kinds of small motors. The A requirements plan for a certain type of gears is summarized in the following table. Fixed setup cost for production in any week is $70$ liras and inventory holding cost is $1\mathrm{.}5$ liras per unit per week. Assume that there are no production capacity restrictions. Stockouts are not allowed. $($Ignore unit manufacturing costs of gears in your computations.$)$WeekDemand $($units$)42010305156202040($a$)$ Determine the weekly production quantities by Least Unit Cost method. What is the cost of this solution?$($b$)$ Determine the weekly production quantities by Part Period Balancing. What is the cost of this solution?$($c$)$ Is any of the solutions in part $($a$)$ or part $($b$)$ optimal? Explain.$($d$)$ Suppose that the maximum number of units of gears that can be stored in the warehouse of the firm is $80.$ Apply the two$-$stage heuristic approach to obtain a solution to this capacitated lot sizing problem and calculate the sum of the total setup and total holding costs for the solution.