Break even and profitability analysis is a classical and widely used
topic in business analysis. Break-Even Point or point of equilibrium is the
point of sales volume making neither a profit nor a loss. It is a valuable
number to know. Traditional break-even analysis is used to determine how much
sales volume your business needs to start making a profit. In this paper, we
extend the classical break-even point concept by introducing a new notion of
constrained break-even points with respect to prices. In this case, a
traditional method of calculating break even point may fail. For this purpose,
for finding constrained break-even points, we propose an optimization approach
based on solving convex and nonconvex
optimization problems. Convex minimization and convex maximization algorithms
are used. We show that global minimum, local maximum, and stationary points of
both problems are the constrained break-even points with respect to price. The
proposed approaches illustrated on some fictitious business examples providing
numerical results.
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