Problem $6-25($Algo$)$ Prepare and Interpret Income Statements; Changes in Both Sales and Production; Lean Production $[$LO$6-1,$ LO$6-2,$ LO$6-3]$Starfax$,$ Incorporated, manufactures a small part widely used in various electronic products. Results for the first three years of operations were as follows $($absorption costing basis$)$: Year $1$Year $2$Year $3$Sales$ $812,800$$ $650,240$$ $812,800$Cost of goods sold$589,280406,400629,920$Gross margin$223,520243,840182,880$Selling and administrative expenses$193,040182,880172,720$Net operating income $($loss$)$$ $30,480$$ $60,960$$ $(\backslash 10,160\backslash )$In the latter part of Year $2,$ a competitor went out of business and dumped a large number of units on the market. As a result, Starfaxs sales dropped by $20\%$ during Year $2$ even though production increased during the year. Management had expected sales to remain constant at $50,800$ units; the increased production was designed to provide a buffer of protection against unexpected spurts in demand. By the start of Year $3,$ management had excess inventory and realized growth in demand was unlikely; thus, it cut back production throughout the year, as shown below: Year $1$Year $2$Year $3$Production in units$50,80060,96040,640$Sales in units$50,80040,64050,800$Additional information about the company follows:The companys plant is highly automated. Variable manufacturing expenses $($direct materials, direct labor, and variable manufacturing overhead$)$ total only $$2\mathrm{.}00$ per unit, and fixed manufacturing overhead expenses total $$487,680$ per year.A new fixed manufacturing overhead rate is computed each year based on that year's actual fixed manufacturing overhead costs divided by the actual number of units produced.Variable selling and administrative expenses were $$1$ per unit sold in each year. Fixed selling and administrative expenses totaled $$140,640$ per year.The company uses a FIFO inventory flow assumption. $($FIFO means first$-$in first$-$out. In other words, it assumes the oldest units in inventory are sold first.$)$Starfaxs management cant understand why profits doubled during Year $2$ when sales dropped by $20\%$ and why a loss was incurred during Year $3$ when sales recovered to previous levels.Required:$1.$ Prepare a variable costing income statement for each year$\mathrm{.}2.$ Refer to the absorption costing income statements above.Compute the unit product cost in each year under absorption costing. Show how much of this cost is variable and how much is fixed.Reconcile the variable costing and absorption costing net operating income figures for each year$\mathrm{.}5$b$.$ If Lean Production had been used during Year $2$ and Year $3,$ what would the companys net operating income $($or loss$)$ have been in each year under absorption costing?