Question

A hair salon offers three services: haircuts, color treatment, and styling. The salon charges \(\$ 40\) for a cut, \(\$ 65\) for color, and \(\$ 30\) for styling. Last month, the salon sold 68 haircuts, 34 color treatments, and 22 styling sessions. If the salon's costs for the month totaled \(\$ 2,843,\) what was its profit? \(\left[\mathrm{LO}_{12}, 1\right]\)

Short answer

Profit is \(\$2747\).

Step-by-step solution

Calculate Total Revenue from Haircuts

The salon charged \(\\(40\) for each haircut and sold 68 haircuts. Thus, the total revenue from haircuts is calculated as follows: \[68 \times 40 = \\)2720\].

Calculate Total Revenue from Color Treatments

The amount charged for each color treatment is \(\\(65\) and 34 of them were sold. Therefore, the revenue from color treatments is: \[34 \times 65 = \\)2210\].

Calculate Total Revenue from Styling Sessions

For styling, the salon charged \(\\(30\) per session and sold 22 sessions. The total revenue from styling is thus: \[22 \times 30 = \\)660\].

Calculate Total Revenue

Add the revenue from haircuts, color treatments, and styling sessions to calculate the total revenue, which is: \[2720 + 2210 + 660 = \$5590\].

Calculate Profit

Subtract the total cost of the month from the total revenue to determine the profit: \[5590 - 2843 = \$2747\].

Key concepts

Total Revenue

In the world of business, especially in a service-based industry like a hair salon, understanding the concept of Total Revenue is crucial. Total revenue represents the complete earnings a business makes from its services before any costs are subtracted.
To calculate total revenue, you multiply the number of units sold by the price per unit. For example, in the case of hair salon services, if a salon offers haircuts at \(40 each and they sell 68 haircuts, the total revenue from haircuts alone would be obtained by multiplying 68 haircuts by \)40, giving us \(68 \times 40 = \$2720\).
This method applies similarly to other services the salon provides. Each service has a set price, and the total revenue for that service is calculated by multiplying the price by the quantity sold. This helps businesses understand how much they earn from different services and make informed decisions to increase revenue.

Hair Salon Services

Hair salons typically provide a variety of services such as haircuts, color treatments, and styling sessions. Each of these services caters to different customer needs and preferences. By diversifying the services offered, salons can attract a wider customer base and increase their total revenue.
- **Haircuts**: A basic service that every salon offers. Typically priced lower than specialized treatments, but due to volume, can significantly contribute to revenue.
- **Color Treatments**: These are more complex and often cost more due to the skills and products required. While fewer clients might opt for color treatments compared to haircuts, they still contribute a substantial part of the total revenue.
- **Styling Sessions**: Often chosen for special occasions, styling can add another revenue stream. Though sold in lower volumes, it complements other services that the salon offers.
Understanding how each service contributes to the total revenue is vital in microeconomic terms as it helps in pricing strategy and service optimization tailored to customer demand.

Cost Analysis

Cost analysis is an integral part of running any business. It involves calculating and monitoring all the expenses involved in providing a service or producing a product. For a hair salon, costs could include anything from wages for salon staff, rent, utilities, to the cost of shampoos, conditioners, and other styling products.
In the given exercise, the total cost for the month is given as \(\$2843\). By understanding and managing these costs, a salon can assess how these expenses compare to their total revenue. If the costs are high relative to revenue, then profit margins shrink.
A good cost analysis helps businesses to:

• Identify areas where they can cut costs without compromising on service quality.
• Set accurate pricing for various services to cover costs and ensure profitability.
• Make informed decisions about expansion or introduction of new services.

Microeconomic Problem Solving

Microeconomic problem solving enables businesses like hair salons to navigate challenges and make decisions that affect their economic outcomes. This involves analyzing how individuals and businesses make choices on resource allocation and pricing.
- **Pricing Strategy**: Calculations involving total revenue and costs provide insights into effective pricing strategies. The salon can choose prices for haircuts, color treatments, and styling that not only cover costs but maximize profits.
- **Supply and Demand Analysis**: Understanding the demand for each service helps the salon optimize their service offerings. For instance, if color treatments are highly demanded, the salon could choose to invest more in color-related training for staff.
By addressing these microeconomic issues, hair salons can optimize their operational efficiency, meet customer needs more effectively, and ultimately improve their profitability. Effective microeconomic problem solving empowers businesses to respond to changes in the market and customer base swiftly.