Question

If the contribution margin per unit is \(\$ 15\) and it takes \(3.0\) machine hours to produce the unit, the contribution margin per unit of limited resource is: a. \(\$ 25\). c. \(\$ 45\). b. \(\$ 5\). d. No correct answer is given.

Short answer

The contribution margin per unit of limited resource is \$5 (option b).

Step-by-step solution

Understand the Problem

The exercise requires finding the contribution margin per unit of a limited resource, given that the contribution margin per unit is $15 and it takes 3.0 machine hours to produce each unit. The limited resource in this case is the machine hours.

Calculate Contribution Margin Per Unit of Machine Hour

The contribution margin per unit of limited resource (machine hour) can be calculated by dividing the contribution margin per unit by the number of machine hours per unit. Mathematically, this can be written as: \[ \text{Contribution Margin Per Unit of Limited Resource} = \frac{\text{Contribution Margin Per Unit}}{\text{Machine Hours Per Unit}} \] Substitute the given values: \[ \text{Contribution Margin Per Unit of Limited Resource} = \frac{15}{3.0} = 5 \] Thus, the contribution margin per unit of machine hour is \$5.

Compare to Given Answers

Examine the possible answers: a. \\( 25, c. \\) 45, b. \\( 5, d. No correct answer is given. Based on the calculation, option b (\\)5) is the correct answer.

Key concepts

Limited Resource

In business and economics, the term "limited resource" is often used to describe a constraint that restricts the production capacity of a company. A limited resource can be anything from raw materials, labor, or, as in our example, machine hours. When businesses identify a limited resource, they need to decide how best to allocate it.

Understanding the impact of a resource constraint is essential for maximizing profitability. Companies strive to allocate their limited resources to products or services that generate the highest contribution margin per unit. In essence, it's about getting the most financial gain from every unit of the scarce resource used.

• Allows businesses to prioritize products that give the highest return per unit of resource.
• Helps indecision-making processes, especially in production planning.

When faced with a resource constraint, focusing on contribution margin per unit resource ensures that the company makes the most out of limited capacities.

Machine Hours

Machine hours are a measure of how long a machine operates to produce a unit of product. In manufacturing, machine hours can be a critical factor, especially when machines are a bottleneck in production. Each product requires a certain amount of machine time, which is often a limited and valuable resource.

In scenarios where machine hours are limited, it's crucial to calculate how much contribution margin each hour of machine time brings. This helps companies decide on which products to prioritize and how to schedule production to maximize profit.

• A critical component in calculating the efficiency of production processes.
• Helps identify bottlenecks and make informed scheduling decisions.

By evaluating the contribution margin per machine hour, companies can optimize machine usage and ensure that the most profitable products make it to market.

Unit Economics

Unit economics refers to evaluating the financial viability of a unit of product. It involves analyzing revenue and cost per unit, providing insight into the profitability of individual products. The contribution margin is a key part of unit economics, as it shows how much each unit contributes to covering fixed costs after variable costs are accounted for.

By understanding unit economics, businesses can make more informed decisions about pricing, scaling operations, and prioritizing production. In cases of limited resources, knowing the unit economics helps to determine how effective each unit is in generating profit relative to the resource used.

• Foundation for setting prices and evaluating business scalability.
• Effective for determining which products are profitable and which are not.

A close examination of unit economics allows companies to maintain a more sustainable business model, ensuring that every unit produced aids in achieving overall financial goals.