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== Explicit formal analysis of the multi-product case ==
== Explicit formal analysis of the multi-product case ==


[[Break-even-Analyse|Break-even-analyses]] for [[Multi-product break-even-analysis|multi-product]] cases have to deal with joint fixed costs for several products, and variable costs, fixed costs and sales revenues that can be linked directly to the products. Measuring the multiple products by a single index is one way to solve the problem; allocating (joint) fixed costs to the different products is another way.<br>
[[Break-even-Analyse|Break-even-analyses]] for [[Multi-product break-even-analysis|multi-product]] cases have to deal with joint fixed costs for several products (or '''common fixed costs'''), and variable costs, fixed costs and sales revenues that can be linked directly to the products '''(direct costs)'''. Measuring multiple products by a single index is one way to solve the problem; allocating (joint) fixed costs to the different products is another way.<br>
Such simplifications are useful ways to deal with complex problems in many situations but sometimes simple approaches neglect critical information and exclude useful solutions. A more sophisticated solution can make the difference in a competitive environment. At least, the more sophisticated solution serves as a benchmark and allows both quantitative and qualitative assessments of other approaches. We introduce the explicit analysis of the multi-product case in the following steps:<br>
Such simplifications are useful ways to deal with complex problems in many situations but sometimes simple approaches neglect critical information and exclude useful solutions. A more sophisticated solution can make the difference in a competitive environment. At least, the more sophisticated solution serves as a benchmark and allows both quantitative and qualitative assessments of other approaches. We introduce the explicit analysis of the multi-product case in the following steps:<br>


* Analysis of the case of two products with joint fixed costs
* Analysis of the case of two products with joint (or common) fixed costs
* Analysis of the case of two products with joint and individual fixed costs
* Analysis of the case of two products with joint and individual (or direct) fixed costs
* Analysis of the two-product case with capacity restrictions
* Analysis of the two-product case with capacity restrictions
* Analysis of the multi-product case with capacity restrictions.
* Analysis of the multi-product case with capacity restrictions.


A detailed analysis of theses cases is available in Schweitzer/Troßmann (1998) and Schweitzer/Troßmann/Lawson (1992). The [[Accounting exercises 4: Break-even-Analysis|exercise pages]] offer useful examples.<br>
A detailed analysis of theses cases is available in Schweitzer/Troßmann (1998) and Schweitzer/Troßmann/Lawson (1992). The [[Accounting exercises 4: Break-even-Analysis|exercise pages]] offer useful examples.<br>


== The case of two products with joint fixed costs ==
== The case of two products with joint fixed costs ==
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