Chapter 4.3, Problem 29PPS

(a)

To determine

To find: The matrix for the number of each type of room at each bed and breakfast and room cost matrix.

Answer to Problem 29PPS

The matrix for the number of each type of room at each bed and breakfast is $\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 1\\ 4& 3& 0\end{array}\right]$ and room cost matrix is $\left[\begin{array}{l}220\\ 250\\ 360\end{array}\right]$ .

Explanation of Solution

Given:

The cost of room with single bed is $220 a night.

The cost of room with two beds is $250 a night.

The cost of suite is $360

Calculation:

The matrix for the number of each type of room at each bed and breakfast is written as,

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

The room cost matrix is written as,

  $\left[\begin{array}{l}220\\ 250\\ 360\end{array}\right]$

Thus, the matrix for the number of each type of room at each bed and breakfast is $\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 1\\ 4& 3& 0\end{array}\right]$ and room cost matrix is $\left[\begin{array}{l}220\\ 250\\ 360\end{array}\right]$ .

(b)

To determine

To find: The matrix for total daily income.

Answer to Problem 29PPS

The matrix for total daily income is $\left[\begin{array}{l}1880\\ 1550\\ 1630\end{array}\right]$ .

Explanation of Solution

Given:

The cost of room with single bed is $220 a night.

The cost of room with two beds is $250 a night.

The cost of suite is $360

Calculation:

The matrix is calculated as,

  $\left[\begin{array}{ccc}3\times 220& 2\times 250& 2\times 360\\ 2\times 220& 3\times 250& 1\times 360\\ 4\times 220& 3\times 250& 0\times 360\end{array}\right]=\left[\begin{array}{l}1880\\ 1550\\ 1630\end{array}\right]$

Thus, the matrix for total daily income is $\left[\begin{array}{l}1880\\ 1550\\ 1630\end{array}\right]$ .

(c)

To determine

To find: The total daily income.

Answer to Problem 29PPS

The total daily income is $\$5060$ .

Explanation of Solution

Given:

The cost of room with single bed is $220 a night.

The cost of room with two beds is $250 a night.

The cost of suite is $360

Calculation:

Calculate the total cost.

  $1880+1550+1630=\$5060$

Thus, the total daily income is $\$5060$ .