Lynch Company manufactures and sells a single product. The following costs were incurred during the company's first year of operations:

$\backslash$table$[[$Variable costs per unit:$],[$Manufacturing:$],[$Direct materials,,$12],[$Direct labor,$$,3],[$Variable manufacturing overhead,$$,1],[$Variable selling and administrative,$$,1],[$Fixed costs per year:$],[$Fixed manufacturing overhead,,$000],[$Fixed selling and administrative,,$000]]$

During the year, the company produced $27,000$ units and sold $23,000$ units. The selling price of the company's product is $$42$ per unit.

Required:

Assume that the company uses absorption costing:

a$.$ Compute the unit product cost.

b$.$ Prepare an income statement for the year.

Assume that the company uses variable costing:

a$.$ Compute the unit product cost.

b$.$ Prepare an income statement for the year.