I: Break$-$Even Analysis: Determine the minimum dollar volume and unit volume needed to break even and complete graph $1.$ Label each of the boxes in the graph

A number of assumptions underlie the basic break$-$even model. Notably, costs and revenue are shown as straight lines. They are shown to increase linearly $-$ that is$,$ in direct proportion to the volume of units being produced. However, neither fixed costs nor variable costs $($nor$,$ for that matter, the revenue function$)$ need be a straight line. For example, fixed costs change as more capital equipment or warehouse space is used; labor costs change with overtime or as marginally skilled workers are employed; the revenue function may change with such factors as volume discounts.

The formulas for the break$-$even point in units and dollars for a single product are shown below. Let:

$)$

The break$-$even point occurs where total revenue equals total costs. Therefore:

$TR=TCorPx=F+Vx$

Stephens, Inc., wants to determine the minimum dollar volume and unit volume needed at its new facility to break even.

Approach

The firm first determines that it has fixed costs of $$10,000$ this period. Direct labor is $$1\mathrm{.}50$ per unit, and material is $$\mathrm{.}75$ per unit. The selling price is $$4\mathrm{.}00$ per unit.

Calculate the break$-$even point in dollars and in units $($must include steps and show your work$)$: