Byron's Manufacturing makes tables. Demand for the next four months and capacities of the plant are shown in the table below. Unit cost on regular time is $$40.$ Overtime cost is $150\%$ of regular time cost. Subcontracting is available in substontial quantity at $$75$ per unit. Holding costs are $55$ per table per month: back orders cost the firm $$10$ per unit per month. Byron's management believes that the fronsportation algorithm con be used to optimize this scheduling problem. The firm has $50$ units of beginning inventory and anticipates no ending inventory.MarchDemand:$400$Regular capacity:$400$Overtime capacity:$100$Subcontract cap:$150$AprilDemand:$600$Regular capacity:$400$Overtime capacity:$100$Subcontract cap:$50$MayDemand:$600$Regular capacity:$400$Overtime capacity:$100$Subcontract cap:$50$JuneDemand:$700$Regular capacity:$400$Overtime capacity:$100$Subcontract cap:$50$a$.$ How many units will be produced on regular time in June?b$.$ How many units will be produced by subcontracting over the four$-$monthperiod?c$.$ What will be the inventory at the end of April?d$.$ What will be total production from all sources in April?e$.$ What will be the total cost of the optimum solution?f$.$ Does the firm utilize the expensive options of subcontracting and backordering? When: why?