Product-Mix Decisions With Capacity Constraints

Learning Objective 4 Know how to choose which products to produce when there are capacity constraints

select the product with the highest contribution margin per unit of the limiting resource

We now examine how the concept of relevance applies to product-mix decisions, the decisions managers make about which products to sell and in what quantities. These decisions usually have only a short-run focus because they typically arise in the context of capacity constraints that can be relaxed in the long run. In the short run, for example, BMW, the German car manufacturer, continually adapts the mix of its different models of cars (for example, 328i, 528i, and 750i) to fluctuations in selling prices and demand.

To determine product mix, managers maximize operating income, subject to constraints such as capacity and demand. Throughout this section, we assume that as short-run changes in product mix occur, the only costs that change are costs that are variable with the number of units produced (and sold). Under this assumption, the analysis of individual product contribution margins provides insight into the product mix that maximizes operating income. The same basic concepts apply in the more general cases except that we then need to consider contribution margins based on variable costs at different levels of the cost hierarchy.

Example 4

Power Recreation assembles two engines, a snowmobile engine and a boat engine, at its Lexington, Kentucky, plant. The following table shows the selling prices, costs, and contribution margins of these two engines:

The table depicts the selling prices, costs, and contribution margins for snowmobile and boat engines. The details of the table are as follows:

1. Selling price

Snowmobile engine: 800 dollars
Boat engine: 1,000 dollars

2. Variable cost per unit

Snowmobile engine: 560 dollars
Boat engine: 625 dollars

3. Contribution margin per unit

Snowmobile engine: 240 dollars
Boat engine: 375 dollars

4. Contribution-margin percentage

Snowmobile engine, 240 dollars divided by 800 dollars: 30 percent
Boat engine, 375 dollars divided by 1,000 dollars: 37.5 percent

Only 600 machine-hours are available daily for assembling engines. Additional capacity cannot be obtained in the short run. Power Recreation can sell as many engines as it produces. The constraining resource, then, is machine-hours. It takes 2 machine-hours to assemble one snowmobile engine and 5 machine-hours to assemble one boat engine. What product mix should Power Recreation’s managers choose to maximize operating income?

In terms of contribution margin per unit and contribution-margin percentage, the data in Example 4 shows that boat engines are more profitable than snowmobile engines. Should Power Recreation produce and sell boat engines? Not necessarily. The following table shows that managers should choose the product with the highest contribution margin per unit of the constraining resource (factor). That’s the resource that restricts or limits the production or sale of products.

A table shows computations for finding the highest contribution margin per unit of the constraining resource.

The table depicts contribution margin information for snowmobile and boat engines. The details of the table are as follows:

1. Contribution margin per unit

Snowmobile engine: 240 dollars
Boat engine: 375 dollars

2. Machine-hours required to assemble one unit

Snowmobile engine: 2 machine-hours
Boat engine: 5 machine-hours

3. Contribution margin per machine-hour

Snowmobile engine, 240 dollars per unit divided by 2 machine-hours per unit: 120 dollars per machine hour
Boat engine, 375 dollars per unit divided by 5 machine-hours per unit: 75 dollars per machine hour

4. Total contribution margin for 600 machine-hours

Snowmobile engine, 120 dollars per machine-hour times 600 machine-hours: 72,000 dollars
Boat engine, 75 dollars per machine-hour times 600 machine-hours: 45,000 dollars

The number of machine-hours is the constraining resource in this example, and snowmobile engines earn more contribution margin per machine-hour $begin inline style left parenthesis straight $ 120 divided by text machine end text short dash back space text hour end text right parenthesis end style$ compared with boat engines $inline style begin inline style left parenthesis straight $ 75 divided by text machine end text short dash back space text hour end text right parenthesis straight. end style$ Therefore, choosing to produce and sell snowmobile engines maximizes total contribution margin ($72,000 vs. $45,000 from producing and selling boat engines) and operating income. Other constraints in manufacturing settings can be the availability of direct materials, components, or skilled labor, as well as financial and sales factors. In a retail department store, the constraining resource may be linear feet of display space. Regardless of the specific constraining resource, managers will maximize total contribution margin by choosing products with the highest contribution margin per unit of the constraining resource.

In many cases, a manufacturer or retailer has the challenge of trying to maximize total operating income for a variety of products, each with more than one constraining resource. Some constraints may require a manufacturer or retailer to stock minimum quantities of products even if these products are not very profitable. For example, supermarkets must stock less-profitable products, such as paper towels and toilet paper, because customers will only shop at supermarkets that carry a wide range of products. To determine the most profitable product mix, the manufacturer or retailer must maximize total contribution margin in the face of many constraints. Optimization techniques, such as linear programming, discussed in the appendix to this chapter, help solve these more complex problems.

At the same time, managers work to relieve the bottleneck constraint to increase output and contribution margin. Can the available machine-hours for assembling engines be increased beyond 600, for example, by reducing idle time? Can the time needed to assemble each snowmobile engine (2 machine-hours) or each boat engine (5 machine-hours) be reduced, for example, by reducing setup time and processing time of assembly? Can some of the assembly operations be outsourced to allow more engines to be built? We address these questions in the following section.

Try It! 12-3

The Gannett Company provides landscaping services to corporations and businesses. All its landscaping work requires Gannett to use landscaping equipment. Its landscaping equipment has the capacity to do 14,000 hours of landscaping work. It currently anticipates getting orders that would utilize 13,200 hours of equipment time. Gannett charges $115 per hour for landscaping work. Cost information for the current expected activity level is as follows:

The table depicts cost information for the current activity level for Gannett Company. The details of the table are as follows:

1. Revenues, 115 dollars times 13,200 hours: 1,518,000 dollars

2. Variable landscaping costs (largely labor), which vary with the number of hours worked, 60 dollars per hour times 13,200 hours: 792,000 dollars

3. Fixed landscaping costs: 110,000 dollars

4. Variable marketing costs, 5 percent of revenues: 75,900 dollars

5. Fixed marketing costs: 74,000 dollars

6. Total costs: 1,051,900 dollars

7. Operating income: 466,100 dollars

In order to fill its available capacity, Gannett’s salespersons are trying to find new business. Russell Corporation wants Gannett to do 4,600 hours of landscaping work for $100 per hour. Variable landscaping costs for the Russell Corporation order are $50 per hour and variable marketing costs are 5% of revenues. Gannett can accept as much or as little of the 4,600 hours of Russell’s landscaping work. What should Gannett Corporation do?