A manufacturing company produces widgets with the following production costs:

Cost of raw materials per unit: $$5$

Labor cost per unit: $$3$

Overhead cost per unit: $$2$

The company sells each widget for $$20.$ Determine the following:

a$)$ Total variable cost per unit.

b$)$ Total fixed cost per unit.

c$)$ Break$-$even point in units.

d$)$ Profit at a production level of $1,000$ units.