Question

You own a factory that hand-manufactures cardigans and pullover sweaters. Both use the same amount of material, but the cardigan requires 2 labor hours to produce, while the pullover requires only 1.5 hours. The cardigan sells for $50 and has variable costs of $28. The pullover sells for $45 and has variable costs of $20. You're only able to employ workers for 2,000 total hours per month.

a. What is the unit of constrained resource in this scenario, and how much contribution margin does each sweater type provide per unit of constrained resource?

b. How many of each sweater type should this factory produce?

Answer 1

When a company wants to maximize their profits when resources are limited, a company must produce the product/products with the highest contribution margin per unit of limited resource. The two steps involved in selecting the most profitable use of the limited resource are follows.

Step 1: Calculate contribution margin per unit of product. Contribution margin per unit can be calculated by deducting all variable costs per unit from the sales per unit.

Step 2: The contribution margin (CM) per unit of the scarce resource is calculated for each product by dividing the amount of resource required for each unit of product into the contribution margin.

CM per Limited resource =

Contribution margin per unit of product / Resource needed per unit of product

Step 3: Select the product with the largest contribution margin per unit of limited resource. This is the product for which the company will produce the most units.

Applying the above steps in the given problem:

In this problem the limiting factor is shortages in labor, so the unit of constrained resource in this scenario will be “Labor Hours”

Step 1:

Calculation of Contribution margin per unit :

	Cardigans (2 Hours)	Pullover (1.5 Hours)
Sales	50	45
Less : Variable Cost	28	20
= Contribution margin per unit	22	25

Step 2:

Calculation of CM per limited resource:

CM per limited resource for cardigans = 22 /2

                                      = $11

CM per limited resource for pullover = 25 /1.5

                                      = $16.67

Pullover should be produced because it generates ($16,67 per labor hour) a higher contribution margin per limited resource (labor hour) than Cardigans ($11 per labor hour ) is produced.

Since there is no minimum number of units of either product, Company should produce only Pullover because it generates a higher contribution margin per hour of production labor used in production. To calculate the number of units of pullover, divide the time required to produce each unit of pullover into the total available hours:

No. of pullover should be produced by the company = 2000 Hours / 1,5 Hours

                                                                                      = 1333 Units

ANSWERS

a. Since the limiting factor is shortages in labor, so the unit of constrained resource in this scenario will be “Labor Hours”. And the contribution margin does each sweater type provide per unit of constrained resource will be

Cardigan - $11

Pullover - $16.67

b. No. of pullover should be produced by the company = 2000 Hours / 1,5 Hours

                                                                                      = 1333 Units