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The cost volume profit analysis has a rogue assumption. This rogue assumption believes that the cost volume profit analysis is completely scalable. We know that this is not the case. We operate in a finite world and have finite resources. We show this in our analysis when we write down the relevant range within which this analysis is valid. So, while performing contribution analysis, we also have to pay attention to the constraints that we have while maximizing production. This is what this article will explain in more detail.
In real life, we cannot go on producing the products with maximum contribution margin. Our sales of this product will be limited by the size of the market. Our production will also be limited by the size of resources. What if production requires a certain number of hours on a particular machine and we have limited number of hours on that machine. We will have to optimize our contribution analysis accordingly.
In this case, we have to shift the focus of our analysis. Instead of focusing our analysis on maximizing the contribution margin, we must focus on maximizing the margin while making minimal use of the resources. This technique is fairly recent in managerial accounting. It has been introduced as an improvement over the older versions of contribution analysis.
In a single constraint contribution, we will try to maximize the output per unit of constraint. For example, A produces $100 of contribution but requires 4 hours on the machine, but B produces $70 in 2 hours on the machine. So here, we will divide the contribution margin, not by sales, but with the hours that it spends on the machine.
So A has a per hour contribution of $25 whereas B has a per hour contribution of $35. Hence, we must allocate more machine hours to B, A must only get the residual machine hours.
Firms usually work with multiple constraints. They can have constraints on sales, on capacity, on know how and many such things. In such case, the decision to optimize the production and sales mix goes beyond the purview of managerial accounting. There is a separate science called operations research which has been developed for this purpose. There are techniques like linear programming problem that help us solve this question. However, since they are beyond the scope of this course and this subject we will not delve into their details.
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