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# Contribution Margin per Unit of the Constrained Resource

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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

**Production Has to Be Maximized Within Constraints:**

In real life, we cannot go on producing the products with maximum contribution margin. The size of the market will limit our sales of this product. Our production will also be limited by the size of resources. What if production requires a certain number of hours on a machine and we have limited number of hours on that machine. We will have to optimize our contribution analysis accordingly.

**Shift of Focus:**

In this case, we must 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 recent in managerial accounting. It has been introduced as an improvement over the older versions of contribution analysis.

**Single Constraint Contribution:**

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.

**Multi-Constraint Contribution:**

Firms usually work with multiple constraints. They can have constraints on sales, on capacity, on knowledge 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.

**Types of constraints**

A constraint limits the output that an entity can produce. Thus, a machine that is only able to produce a certain amount of a crucial part will limit sales of the final products that incorporate that part. When viewing such constraints, the key issue is whether an expansion of the constraint could result in more sales. If so, proper management of the constraint can lead to more profits.

Given the importance of the constraint concept, it is of great importance to understand the types of constraints to which a business may be subjected. Consider the following:

. A company may have worked through all its constraint issues, in which case obtaining more orders from the market is considered the constraint. This constraint can be overcome by offering better deals to customers to spur sales growth.__Marketplace constraint__. When employees hold a belief that causes them to act in a certain way, this is called a paradigm constraint, and can impact a process to such an extent that the belief is considered a constraint. An example of such a constraint is the belief that the only good work station is one humming along at 100% of capacity, even though there is not enough demand to justify so much work. The result could be the divergence of resources away from the true constraint (perhaps a machine) resulting in suboptimal use of the actual constrained resource.__Paradigm constraint__. A machine that has a large amount of work-in-process in queue in front of it is obviously maxed out, and so could be a constraint.__Physical constraint__. This is a management-imposed guideline for how a process is to be conducted. For example, there may be a rule regarding the minimum batch size that should be run through a machine, or the economic order quantity to be ordered from a supplier, or the quantity of parts that should build up next to a production cell before it is transported to the next production cell. Unless carefully monitored, these policy constraints can interfere with the orderly flow of work through a business. Policy constraints are difficult to find, since you must track backwards to them by observing their effects on the business. It may be equally difficult to eliminate such a constraint, since it may have been used by employees for many years.__Policy constraint____Raw material constraint__When there is not enough of a raw material available to meet all customer orders, the raw material is the constraint. This constraint is most likely to arise when there is excessive demand for a raw material, and where there are not enough substitutes available to replace the raw material.__.__. When the sales process is complex, any step in the process that does not have sufficient resources can result in a reduced level of sales. For example, a shortage in sales engineers can result in too few product demonstrations, and therefore in too few sales being completed.__Sales department constraint__

Management may choose to have a constraint in a place within the company. This happens when the cost of increasing the selected constraint is so high that managing and working around this constraint is the most cost-effective way to run the business. For example, the cost of adding another paint booth may be so high that management would prefer to concentrate on managing every minute of its time and outsourcing all remaining work.

How does a company decide which product is given priority over constrained resources? We must look at how each product uses the constrained resource and maximize contribution margin per hour. Let’s look at an example.

Example – Unlimited Demand

KLI Desks, Inc. makes two types of office desks, Executive and Standing. Both desks require time in the Painting Department, but there are only 172 hours per month available currently in that department. The company can sell as many of each desk as it can make. What is the optimal product mix that would maximize profit each month?

At first glance, it would be tempting to make the standing desk, since it has a higher contribution margin per unit, but with the constraint of the painting department hours will that give KLI Desks the highest monthly contribution margin? To determine if that is true, we don’t need to calculate the contribution margin for all 172 hours. We just need to calculate the contribution margin for one hour for each product and determine which is higher.

If the Executive desk takes 15 minutes to paint, we can make 4 per hour (60/15). We can make 3 of the Standing desk per hour (60/20). Multiply the number of desks that can be made each hour by the contribution margin per desk.

Although the Executive Desk has a lower contribution margin per unit, the increased product per hour results in a higher contribution margin per hour. Therefore, we would only produce Executive desks.

**SELF-CHECK ACTIVITY **

- Explain contribution margin per unit of the constrained resource?
- Describe various type of constrained resource?