Managers are often faced with constrained resources. In those situations, they must decide how to use the resource to generate the most benefit possible. For example, a company may have limited machine capacity, so it can only make a limited amount of its products. In a case like that, the manager must decide which of its products it should use the machine to make. Here's an example. The T-Shirt Maker anticipates demand for 12,000 basic t-shirts at a price of $10 and 3,000 deluxe t-shirts at a price of $14. The company has a capacity of 3,500 machine hours. How many basic t-shirts and how many deluxe t-shirts should the company make? Now to simplify a bit more for this particular illustration, let's first frame this decision as a decision of whether to use the 3,500 machine hours to make basic t-shirts or to make deluxe t-shirts, assuming unlimited demand for both. Recall our decision making framework. First, we define the decision to be made. That decision is which product to make using that constrained resource machine hours. There are two alternatives, make basic shirts or deluxe shirts. Third, we gather the information relevant to making the decision. Well, what information is that? Well, it's the revenues the company would earn and the cost the company would incur under each of those two alternatives. After an analysis we can evaluate and decide which alternative to choose. So, again, we have two alternatives. Alternative 1, use the constrained resource machine hours to make basic t-shirts. Alternative 2 is to use the machine hours to make deluxe t-shirts. The company will generate revenues and incur costs under both alternatives, and it is the difference then that's going to be relevant to making the decision. Note also that the relevant cost here are the variable costs associated with each type of t-shirt. The fixed costs the company incurs are not relevant to the decision because tey will be the same regardless of which type of t-shirt the company uses the machine hours to make. So, we should be able to make this decision by looking at revenues and variable costs, with a contribution margin, for each type of t-shirt without considering the fixed cost. So let's look at the contribution margin of each type of t-shirt. The contribution margin for the basic t-shirt is $3.59. The contribution margin for the deluxe t-shirt is $4.73 per shirt. So at first glance then, it appears that, well, the t-shirt make would rather make the deluxe t-shirts because the contribution margin on a deluxe t-shirt is greater than the contribution margin on a basic t-shirt. But the company has a constrained resource, machine hours, and the two types of t-shirts require a different amount of that constrained resource. It takes 0.231 machine hours to make a basic t-shirt and 0.345 machine hours to make a deluxe t-shirt. Now remember, the company only has 3,500 machine hours to use in making t-shirts and it would like to use those machine hours to generate as much contribution margin as possible. So let's look at how much contribution margin the company would generate under each alternative. What if the company used all 3,500 machine hours to make basic t-shirts? Each basic t-shirt requires 0.231 machine hours to make. So, with 3,500 machine hours, the company can make 15,152 basic t-shirts. With each t-shirt's contribution margin being $3.59, the total contribution margin with this alternate is $54,396. Now alternatively, what if the company used all 3,500 machine hours to make the deluxe t-shirts? Well, each deluxe t-shirt requires 0.345 machine hours to make. So with the 3,500 machine hours, the company can make 10,145 deluxe t-shirts. With each shirt's contribution margin being $4.73, the total contribution margin with this alternative is 47,986. So the company would generate more contribution margin if it used the 3,500 machine hours to make basic t-shirts than if it used them to make deluxe t-shirts. Even though the contribution margin for one basic t-shirt is lower than that for one deluxe t-shirt. Now, why is this the case? Well, because the fact that basic t-shirts use less machine hours means that the company can make more basic t-shirts than deluxe t-shirts with that 3,500 hours. And that additional volume offsets the lower per unit contribution margin on the basic t-shirts. So the company would be better off devoting the constrained resource, machine hours, to making basic t-shirts. Now this all seems to make intuitive sense, right? But recall that our original question was not whether to use all 3,500 machine hours to make basic t-shirts or deluxe t-shirts. Indeed, we don't even have sufficient demand to use all those hours to make the 15,000 basic t-shirts or the 10,000 deluxe t-shirts. Our original question was how many machine hours should it devote to making basic t-shirts? And how many machine hours should it devote to making deluxe t-shirts? Now based on the analysis we just did, it seems that, well, conceptually, maybe the company should make enough basic t-shirts to meet the demand for those shirts, since they seem to be the preferable way to use the machine hours. And then after that point, they can use the remaining machine hours to make as much deluxe t-shirts as it can. Makes sense, right? Okay, well, here's another way to look at or think about this complicated decision, which is more than just a choice between two alternatives. The company only has 3,500 machine hours to use on making t-shirts. It would like to use those machine hours to generate as much contribution margin as possible. So, it would like for each of those 3,500 machine hours to generate as much contribution margin as possible. As a result, they would like to make the product that generates the most contribution margin per machine hour. So, let's see how much contribution margin each type of t-shirt makes per machine hour. If basic t-shirts have a contribution margin of $3.59 and they take 0.231 machine hours each to make, then each machine hour devoted to making basic t-shirts will generate $15.54. The $3.59 divided by the 0.231. And likewise, if deluxe t-shirts have a contribution margin of $4.73 per shirt, and they take 0.345 hours to make, then each machine hour devoted to making deluxe t-shirts will generate $13.71. Or $4.73 divided by 0.345. So would the t-shirt maker rather generate $15.54 for each machine hour or $13.71 for each machine hour? Well, of course it would rather generate $15.54 for each machine hour. So, it's better off to use its machine hours to make as many basic t-shirts as it can sell and then use the remaining machine hours to make deluxe t-shirts. All right, let's keep going. So how many of each type of t-shirt should it plan to make? Well, first, it's going to use as many machine hours as needed to satisfy the demand for the basic t-shirts. Remember its demand, 12,000 t-shirts. Now if each shirt uses 0.231 machine hours, then the company's going to use a total of 2,772 machine hours to make the 12,000 shirts. After using 2,772 machine hours, it has 728 machine hours left over out of 3,500 that were not used to make basic t-shirts. So it uses those hours to make deluxe t-shirts, and it can make 2,110 of them. Now this combination of deluxe and basic t-shirts results in a total contribution margin of $53,060. Now, given the demand for basic t-shirts and the demand for deluxe t-shirts and the limited amount of machine hours available, this is going to be the highest contribution margin the company could generate. When thinking about making a decision about product mix in the face of a constrained resource, we need to determine the contribution margin each product generates per unit of that constrained resource. We should produce the product with the highest contribution margin per unit of constrained resource until demand for that product is satisfied. Then devote that constrained resource to producing the product with the next highest contribution margin per unit of constrained resource. And so on and so on.
