Nicolas Inc. sells a product for $$67$ per unit. The variable cost is $$31$ per unit, while fixed costs are $$222,912.$

Determine $($a$)$ the break$-$even point in sales units and $($b$)$ the break$-$even point if the selling price were increased to $$74$ per unit.

a$.$ Break$-$even point in sales units

$x$ units

b$.$ Break$-$even point if the selling price were increased to $$74$ per unit

$x$ units