\begin{tabular}{l} Suppose Guild produces 5,000 guitars per year. Its \\ average total cost is \( \$ 90 \), and its fixed cost is \( \$ 250,000 \). \\ What is its variable cost? \\ \begin{tabular}{l|}\hline\( \$ 250,000 \) \\ \hline\( \$ 450,000 \) \\ \hline\( \$ 25,000 \) \\ \hline\( \$ 66,000 \)\end{tabular} \\ \hline\( \$ 200,000 \)\end{tabular}

To determine the variable cost, we can use the average total cost formula: \[ \text{Average Total Cost (ATC)} = \frac{\text{Total Cost}}{\text{Quantity}} \] First, calculate the total cost: \[ \text{Total Cost} = \text{ATC} \times \text{Quantity} = 90 \times 5,000 = \$450,000 \] Next, the total cost is made up of fixed costs and variable costs: \[ \text{Total Cost} = \text{Fixed Cost} + \text{Variable Cost} \] We know the fixed cost is \( \$250,000 \): \[ 450,000 = 250,000 + \text{Variable Cost} \] Subtract the fixed cost from the total cost: \[ \text{Variable Cost} = 450,000 - 250,000 = \$200,000 \] So, the variable cost is \( \$200,000 \). Now let's look at some fun and engaging insights! Craft music history lovers will find it fascinating that the electric guitar revolutionized music in the mid-20th century, culminating in iconic bands like The Beatles and Led Zeppelin. These musicians used the guitar to create sounds that laid the groundwork for rock music as we know it today—proof that a simple string instrument can change the world! For budding entrepreneurs dreaming of launching their own guitar-making business, a wise tip is to keep a keen eye on your cost structure. Understanding both fixed and variable costs is crucial to pricing your products effectively. Many new businesses often mistakenly underestimate their variable costs, leading to unexpected losses and a not-so-melodic tune by the end of the fiscal year!