Formal multi-product break-even-analysis: Unterschied zwischen den Versionen

Other linear combinations enable fixed-cost-coverage in a similar way. Together, the corresponding break-even-points build a straight line between the break-even-corner-points, the '''break-even-line,''' as can be seen in the following three-dimensional graph (with x₁ and x₂ as horizontal axes and the profit, contribution and costs at the vertical axis.<br>

In order to facilitate algebraic formulations, we introduce the price vector (p₁, p₂), the variable cost vector (k^v₁, k^v₂), the unit contribution vector (d₁, d₂) and the output vector (x₁, x₂). The break-even-line is defined by the following output vector:

The solution of the two individual conditions results in two break-even-points x₁* and x₂*. Considering for the joint fixed cost leads to two break-even-corner-points x₁** and x₂**. The possible break-even-points lie on the line between these corner-points. The graphical presentation of this case is similar to the previous case without individual fixed costs. However, we adjust the horizontal axes (x₁ and x₂) for the volumes that are necessary to cover the individual fixed costs.<br>  

In a formal way this '''break-even-line''' is captured by the set:<br>

Using vector notation for the capacity restraint, he set of break-even-points is: <br>