A convention planning service has identified three suitable hotels for a convention. The quoted room rates are for single, double, triple, and quadruple occupancy. The current cost for each type of room at each hotel is represented by the matrix $A$ $A = \left[ \begin{array} { l l l }
85 & 91 & 98 \
95 & 103 & 110 \
103 & 109 & 120 \
113 & 121 & 129
\end{array} \right]$ where the columns correspond to each hotel and the rows correspond to single, double, triple, and quadruple occupancy respectively. If room rates are guaranteed not to increase by more than 10% by the time of the convention, what is the maximum rate per room per hotel?
A) $\left[ \begin{array} { l l l }
93.50 & 100.10 & 98.00 \
104.50 & 113.30 & 110.00 \
113.30 & 119.90 & 120.00 \
124.30 & 133.10 & 129.00
\end{array} \right]$
B) $\left[ \begin{array} { l l l }
93.50 & 100.10 & 107.80 \
104.50 & 113.30 & 121.00 \
103.00 & 109.00 & 120.00 \
113.00 & 121.00 & 129.00
\end{array} \right]$
C) $\left[ \begin{array} { l l l }
93.50 & 100.10 & 107.80 \
104.50 & 113.30 & 121.00 \
113.30 & 119.90 & 132.00 \
124.30 & 133.10 & 141.90
\end{array} \right]$
D) $\left[ \begin{array} { l l l }
93.50 & 91.00 & 107.80 \
104.50 & 103.00 & 121.00 \
113.30 & 109.00 & 132.00 \
124.30 & 121.00 & 141.90
\end{array} \right]$
E) $\left[ \begin{array} { l l l }
85.00 & 100.10 & 107.80 \
95.00 & 113.30 & 121.00 \
103.00 & 119.90 & 132.00 \
113.00 & 133.10 & 141.90
\end{array} \right]$

Question

A convention planning service has identified three suitable hotels for a convention. The quoted room rates are for single, double, triple, and quadruple occupancy. The current cost for each type of room at each hotel is represented by the matrix $A$ $A = \left[ \begin{array} { l l l } 
85 & 91 & 98 \
95 & 103 & 110 \
103 & 109 & 120 \
113 & 121 & 129
\end{array} \right]$ where the columns correspond to each hotel and the rows correspond to single, double, triple, and quadruple occupancy respectively. If room rates are guaranteed not to increase by more than 10% by the time of the convention, what is the maximum rate per room per hotel?
A) $\left[ \begin{array} { l l l } 
93.50 & 100.10 & 98.00 \
104.50 & 113.30 & 110.00 \
113.30 & 119.90 & 120.00 \
124.30 & 133.10 & 129.00
\end{array} \right]$
B) $\left[ \begin{array} { l l l } 
93.50 & 100.10 & 107.80 \
104.50 & 113.30 & 121.00 \
103.00 & 109.00 & 120.00 \
113.00 & 121.00 & 129.00
\end{array} \right]$
C) $\left[ \begin{array} { l l l } 
93.50 & 100.10 & 107.80 \
104.50 & 113.30 & 121.00 \
113.30 & 119.90 & 132.00 \
124.30 & 133.10 & 141.90
\end{array} \right]$
D) $\left[ \begin{array} { l l l } 
93.50 & 91.00 & 107.80 \
104.50 & 103.00 & 121.00 \
113.30 & 109.00 & 132.00 \
124.30 & 121.00 & 141.90
\end{array} \right]$
E) $\left[ \begin{array} { l l l } 
85.00 & 100.10 & 107.80 \
95.00 & 113.30 & 121.00 \
103.00 & 119.90 & 132.00 \
113.00 & 133.10 & 141.90
\end{array} \right]$

Quizplus · Accepted Answer

To find the maximum rate per room per hotel, increase each rate by 10%. This is done by multiplying each element in the matrix $A$ by 1.10 (or adding 10% of each element to itself). The correct calculations lead to the matrix in choice C.

A Convention Planning Service Has Identified Three Suitable Hotels for a Convention