Variable costs change per unit of output, and fixed costs are the same (or “fixed”) regardless of how many units are produced. If total costs are expressed as a function of units in the form of a linear equation in y=my+b form, the fixed costs would be the “b” (y-intercept)...

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Variable costs change per unit of output, and fixed costs are the same (or “fixed”) regardless of how many units are produced. If total costs are expressed as a function of units in the form of a linear equation in y=my+b form, the fixed costs would be the “b” (y-intercept) term, and the variable costs would be the “m” (slope) term.

Generally, the profit function is similarly linear, but with the slope representing the profit (selling cost per unit minus production cost, or variable cost per unit). Another difference between the profit function and the cost function is that the “b” (y-intercept) is negative.

For example, if a company’s fixed operating costs are $50, and the unit costs $3 to produce, and these units sell for $8, the cost and profit functions are as follows: y=3x+50 (cost function) and y=5x-50 (profit function, wherein the slope, 5, reflects the revenue per unit: $8-$3).

The point at which the profit function as defined herein equals zero is the break-even point.

An alternative way of doing this is by using the $8 as the slope of the profit function as follows: y=8x-50. In this case, net revenue would be determined by setting this profit function equal to y=3x (reflecting the $3 unit cost). Regardless, algebraic manipulator would yield the same break-even cost.