Resources are finite. A business only has so many man hours, so many square feet, and so much machinery. Over the long term, a company can expand its capacity but in the short term, it must make important decisions in order to maximize profit. Constrained resources require businesses to make decisions about which products to make and in what quantities.

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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 #1 – 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.

What if demand for the desks was limited?

Example #1 – Limited 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 only sell 500 of each desk per month. What is the optimal product mix that would maximize profit each month?

This example is a bit different than the last example because we cannot sell an unlimited number of desks. We can only sell 500 of each desk per month. Therefore, we do not want to make more than 500 of either desk. We know from the previous problem that we should make Executive desks first. How many hours would it take to make 500 Executive desks?

500 desks / 4 desks per hour = 125 hours required

There are 172 hours available each month which means we can make some Standing desks but how many?

172 total hours – 125 hours for Executive desks = 47 hours remaining

47 hours X 3 Standard desk per hour = 141 Standard desks

We can make 500 Executive desks and 141 Standard Desks to maximize profit. This is only because we can not sell more than 500 of either desk per month.

Final Thoughts

When working with optimal product mix, determine which product will give you the highest contribution margin per hour of constrained resource. Then look to see if there are other constraints, for example, a limit to the number of units of either product that could be sold.

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