Problem 26 - Algebra 2

Question

HOTELS For Exercises 25 and \(26,\) use the costs for an overnight stay at a hotel that are given below. Single Room: \(\$ 60\) weekday; \(\$ 79\) weekend Double Room: \(\$ 70\) weekday; \(\$ 89\) weekend Suite: \(\$ 75\) weekday; \(\$ 95\) weekend Write a \(2 \times 3\) matrix that represents the cost of each room.

Step-by-Step Solution

Answer

Matrix: \[ \begin{bmatrix} 60 & 70 & 75 \\ 79 & 89 & 95 \end{bmatrix} \]

Step 1: Identify the Categories

We are required to create a matrix that categorizes the cost of hotel rooms by type and by day. We have two categorizations: 1. Type of room - Single, Double, Suite 2. Type of day - Weekday, Weekend.

Step 2: Understand the Matrix Dimensions

The problem asks for a \(2 \times 3\) matrix. This means the matrix will have 2 rows and 3 columns. - The rows can represent the type of day (weekdays and weekends).- The columns can correspond to the type of rooms (Single, Double, Suite).

Step 3: Assign Costs to Matrix Entries

We now fill in the matrix with the costs given:- For weekdays: Single room is \\(60, Double room is \\)70, and Suite is \\(75.- For weekends: Single room is \\)79, Double room is \\(89, and Suite is \\)95.

Step 4: Construct the Matrix

Now, we arrange the costs into the matrix based on the established orientation:\[\begin{bmatrix}60 & 70 & 75 \79 & 89 & 95 \end{bmatrix}\]- The first row represents weekday costs, and the second row represents weekend costs. The columns represent Single, Double, and Suite rooms respectively.

Key Concepts

Hotel Room Costs

Understanding hotel room costs is essential, especially if you're planning a stay or simply analyzing expenses for data-driven decision-making. Hotel room costs vary based on several factors:

• Room Type: Different types of rooms, such as single, double, and suite, each have distinct costs associated with them.
• Time of Stay: The cost often fluctuates between weekdays and weekends due to varying demand levels.

In this exercise, we analyze the costs associated with these different room types during both weekdays and weekends. To efficiently categorize and analyze these costs, we use a matrix representation. This helps to organize and visually display the varying costs in a structured manner. By understanding the breakdown of costs by room type and day, you can get better insights into budgeting and planning an overnight stay at a hotel.

Room Categories

The classification of hotel rooms into categories is crucial for understanding the pricing structure. Each category typically refers to different levels of accommodations and facilities.

• Single Room: Generally designed for one person, these rooms have minimal space and amenities.
• Double Room: Suitable for two guests, often including larger bed sizes or two separate beds.
• Suite: These are larger accommodations offering multiple rooms, and often include luxurious amenities.

In the matrix representation for our exercise, each column corresponds to one of these categories, aiding in segregating costs based on the type of room offered. This classification helps potential guests decide which option fulfills their needs and budget.

Weekday and Weekend Rates

The distinction between weekday and weekend rates can significantly affect hotel room pricing. Hotels adjust these rates in response to demand patterns, often leading to higher prices on weekends.

• Weekday Rates: Typically, these are lower due to less demand as most people travel or vacation over the weekend.
• Weekend Rates: Often higher due to increased demand; hotels might also offer promotions during this time.

Our matrix exercise uses rows to represent these differing rates, allowing us to easily compare how prices change from weekdays to weekends for each room category. Understanding this fluctuation is helpful for consumers planning a more cost-effective stay or for business analyses focused on market trends.