Chapter 3.6, Problem 29PPS

a.

To determine

To find: A matrix for the number of each type of room at each bed and breakfast. Then write a room-cost matrix.

Answer to Problem 29PPS

Matrix is of number of each type of room at each bed and breakfast is

  $N=\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 1\\ 4& 3& 0\end{array}\right]$

Room-cost matrix is

  $C=\left[\begin{array}{c}220\\ 250\\ 360\end{array}\right]$

Explanation of Solution

Given equation:

The wolf family own three beds and breakfasts in a vacation spot. A room with a single bed is $220 per night, a room with two beds is $250 per night, and a suite is $360.

Table of available rooms at a wolf bed and breakfast.

From the given table

We can write a matrix for number of each type of room at each bed and breakfast.

Rows represents number of different types of rooms.

Columns represents different types of rooms.

Therefore,

Number of columns will be 3

Number of rows will be 3

Therefore,

Matrix is of number of each type of room at each bed and breakfast is

  $N=\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 1\\ 4& 3& 0\end{array}\right]$

From given information

The wolf family own three beds and breakfasts in a vacation spot. A room with a single bed is $220 per night, a room with two beds is $250 per night, and a suite is $360.

There will be three rows each row represents different types of rooms.

Column represents the rent for each type of room.

Room-cost matrix is

  $C=\left[\begin{array}{c}220\\ 250\\ 360\end{array}\right]$

b.

To determine

To find: Matrix for total daily income, assuming that all the rooms are rented.

Answer to Problem 29PPS

Daily income matrix is $\left[\begin{array}{c}1880\\ 1550\\ 1630\end{array}\right]$

Explanation of Solution

Given equation:

The wolf family own three beds and breakfasts in a vacation spot. A room with a single bed is $220 per night, a room with two beds is $250 per night, and a suite is $360.

Table of available rooms at a wolf bed and breakfast.

Matrix is of number of each type of room at each bed and breakfast is

  $N=\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 1\\ 4& 3& 0\end{array}\right]$

Room-cost matrix is

  $C=\left[\begin{array}{c}220\\ 250\\ 360\end{array}\right]$

Total daily income matrix is

  $\begin{array}{l}=\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 1\\ 4& 3& 0\end{array}\right]\times \left[\begin{array}{c}220\\ 250\\ 360\end{array}\right]\\ =\left[\begin{array}{c}\left(3\times 220\right)+\left(2\times 250\right)+\left(2\times 360\right)\\ \left(2\times 220\right)+\left(3\times 250\right)+\left(1\times 360\right)\\ \left(4\times 220\right)+\left(3\times 250\right)+\left(0\times 360\right)\end{array}\right]\\ =\left[\begin{array}{c}660+500+720\\ 440+750+360\\ 880+750+0\end{array}\right]\\ =\left[\begin{array}{c}1880\\ 1550\\ 1630\end{array}\right]\end{array}$

Therefore,

Daily income matrix is $\left[\begin{array}{c}1880\\ 1550\\ 1630\end{array}\right]$

c.

To determine

To find: Total daily income from all three bed and breakfast.

Answer to Problem 29PPS

Total income from all three bed and breakfast $=\$5060$

Explanation of Solution

Given equation:

The wolf family own three beds and breakfasts in a vacation spot. A room with a single bed is $220 per night, a room with two beds is $250 per night, and a suite is $360.

Table of available rooms at a wolf bed and breakfast.

Daily income matrix is $\left[\begin{array}{c}1880\\ 1550\\ 1630\end{array}\right]$

Each row represents income from each bed and breakfast

Therefore,

Total income from all three bed and breakfast $=1880+1550+1630$

  $\Rightarrow$ Total income from all three bed and breakfast $=\$5060$