Lehighton Chalk Company manufactures sidewalk chalk. which it sells online by the box at $$24$ per unit. Lehighton uses an actual costing system, which means that the actual costs of the direct material, direct labor, and manufacturing overhead are entered into work$-$in$-$process inventory. The actual application rate for manufacturing overhead is computed each year, actual manufacturing overhead is divided by actual production $($in units$)$ to compute the application rate. Information for Lehighton's first two years of operations is as follows:

$\backslash$table$[[,$Year $1,$Year $2],[$Sules $($in units$),2,300,2,300],[$Production $($in units$),2,800,1,800],[$Preduction Costs:,,$],[$Variable manufacturing costs,$$13,160,48,460],[$Fixed manufacturing costs,$15,960,15,960],[$Selling and Administrative costs:,,$],[$Variable$,9,200,9,200],[$Fixed$,8,200,8,200]]$

Lehighton Chalk Company Selected Bulance Sheet Informatior Bused on absorption costing End of Year $1$ End of Year $2$ Finished$-$goods inventory Retained carnings

$$5,200$

# $0$

$8,380,13,860$

Based $on$ variable costing End $of$ Year $1$ End $of$ Year $2$

Finished$-$goods inventory $$2,350,$$$0$

Retained earnings $5,530,13,860$

Lehighton Chalk Company had $ng$ beginning $or$ ending work$-$in$-$process inventories for either year.

$(1)$ Prepare operating income statements for both years based on absorption costing.

$(2)$ Prepare operating income statements for both years based on variable costing.

$(3)$ Prepare a numerical reconciliation of the difference in income reported under the two costing methods used in requirements I and $2.$