Question

Isabella runs a pet salon. She is currently grooming 125 dogs per week. If instead of grooming 125 dogs, she grooms 126 dogs, she will add $\mathrm{\$}68.50$ to her costs and $\mathrm{\$}60.00$ to her revenues. What will be the effect on her profit of grooming 126 dogs instead of 125 dogs?

Short answer

The profit will decrease by $\mathrm{\$}8.50$.

Step-by-step solution

Calculate the Additional Revenue

The extra revenue gained by grooming one more dog is stated as $\mathrm{\$}60.00$.

Calculate the Additional Cost

The additional cost of grooming one more dog is given as $\mathrm{\$}68.50$.

Calculate the Profit Difference

By grooming one extra dog, the profit change can be calculated by subtracting the extra cost from the extra revenue. This gives, $\mathrm{\$}60.00-\mathrm{\$}68.50=-\mathrm{\$}8.50$.

Key concepts

Profit Calculation

Profit is an essential measure for any business as it represents the financial gain achieved after covering all costs. Simply put, it's the amount of money left over when you subtract the total costs from the total revenues. In the context of Isabella's pet salon, when we talk about profit for grooming dogs, it refers to the excess of revenue over the costs of grooming those dogs. When considering the effect of grooming an additional dog, it's crucial to calculate how this single extra action influences the profit. If the additional revenue from the extra dog exceeds the additional cost, the profit increases. Conversely, if the additional cost outweighs the additional revenue, the profit decreases. In Isabella's case, she must consider that grooming the 126th dog results in more costs than revenue, leading to a negative impact on her profit.

• Total Profit = Total Revenue - Total Cost
• Change in Profit = Additional Revenue - Additional Cost

Hence, the exercise helps us understand how small changes in operations can significantly influence the overall profitability of a business.

Additional Cost

When a business examines the impact of increasing their production or services by one unit, the additional cost, often called the marginal cost, plays a critical role. It includes all the extra expenses required to produce one more unit of output. For Isabella's pet salon, the additional cost of grooming one more dog encompasses all extra resources used, such as more labor, shampoo, and utilities.In this specific calculation, the additional cost is calculated as $68.50$, representing these incremental expenses. This amount is crucial because it helps the business decide whether the additional unit of production is financially viable. It's a balancing act between spending more to make more and avoiding overstepping into losses.Thus, when Isabella thought about grooming one more dog, she needed to consider:

• Additional utilities and materials
• Potential extra wages or overtime pay
• Overall wear and tear on equipment

Understanding and calculating the additional cost allows a business owner to avoid decisions that could lead to lower profits.

Additional Revenue

In business terms, additional revenue denotes the extra money made from selling an additional unit of a product or service. It's an important concept because it directly affects how much profit can be made from increasing output. For Isabella's salon, the extra revenue from grooming one more dog is $60.00$.This additional revenue helps assess if increasing the number of services provided is beneficial. It involves evaluating whether the income from the unit surpasses the added expense to produce or provide it. When examining this for Isabella, the revenue from the 126th dog does not surpass its cost, making it unwise to proceed with that additional service based solely on revenue.Key considerations include:

• Price charged per additional service
• Potential discounts or specials that could affect revenue
• Customer demand impacting the price you can set

Hence, analyzing additional revenue helps Isabella and other business owners understand when it makes financial sense to expand their operations.