Vacation Packages A vacation service has identified four...

Vacation Packages A vacation service has identified four resort hotels with a special all-inclusive package. The quoted room rates are for double and family (maximum of four people) occupancy for 5 days and 4 nights. The current rates for the two types of rooms at the four hotels are represented by $A$. $$A=\left[\begin{array}{llll} 615 & 670 & 740 & 990 \\ 995 & 1030 & 1180 & 1105 \end{array}\right]$$ Room rates are guaranteed not to increase by more than $12 \%$ by next season. What is the maximum rate per package per hotel?

Vacation Packages A vacation service has identified four resort hotels with a special all-inclusive package. The quoted room rates are for double and family (maximum of four people) occupancy for 5 days and 4 nights. The current rates for the two types of rooms at the four hotels are represented by $A$.
$$A=\left[\begin{array}{llll}
615 & 670 & 740 & 990 \\
995 & 1030 & 1180 & 1105
\end{array}\right]$$
Room rates are guaranteed not to increase by more than $12 \%$ by next season. What is the maximum rate per package per hotel?

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Key Concepts

Scalar Multiplication and Percentage Increase

Scalar multiplication involves multiplying every element of a matrix by a constant. In financial or applied contexts, this operation is used to uniformly increase or decrease each entry by a given percentage, effectively scaling the entire dataset by a factor, such as 1.12 for a 12% increase.

Matrix Representation

Matrices are rectangular arrays of numbers arranged in rows and columns that are used to efficiently organize and manipulate related data. They serve as a compact way of representing data sets, where each element's position in a row and column captures its relationship to other data points.

Element-wise Comparison and Maximum Selection

Element-wise comparison is a process where corresponding elements from arrays or matrices are compared to identify extreme values, such as maxima or minima. In many applications, determining the highest value among a set of closely related options is essential for decision-making, making this technique crucial for evaluating optimal choices.

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