Chapter 4.4, Problem 82SR

(a)

To determine

To Find: The matrix that determines the cost of the admission for the residential and the matrix that cost of admission for the non-residential.

Answer to Problem 82SR

The matrix for the resident is $M_1=\left[\begin{array}{cc}3& 6.75\\ 2& 3.50\end{array}\right]$ and for non-residents is $M_2=\left[\begin{array}{cc}4.50& 6.75\\ 3.00& 5.25\end{array}\right]$ .

Explanation of Solution

Given:

The daily admission fees for the residents is shown in Table 1

Table 1

Time of the day	Child	Adult
Before 6:00 PM	$3.00	$4.50
After 6:00 PM	$2.00	$3.50

The daily admission fees for the non-residents is shown in Table 2

Table 2

Time of the day	Child	Adult
Before 6:00 PM	$4.50	$6.75
After 6:00 PM	$3.00	$5.24

Calculation:

The matrix for the daily admission fees for the residents is,

  $M_1=\left[\begin{array}{cc}3& 6.75\\ 2& 3.50\end{array}\right]$

The matrix for the daily admission fees for the non-residents is,

  $M_2=\left[\begin{array}{cc}4.50& 6.75\\ 3.00& 5.25\end{array}\right]$

(b)

To determine

To Find: The matrix that shows the additional cost of the non-residents.

Answer to Problem 82SR

The matrix for the additional cost is $\left[\begin{array}{cc}1.50& 2.25\\ 1.00& 1.75\end{array}\right]$ .

Explanation of Solution

Consider the matrix for the difference between the fees of the two type of residents is,

  $\begin{array}{c}{M}_2-M_1=\left[\begin{array}{cc}4.50& 6.75\\ 3.00& 5.25\end{array}\right]-\left[\begin{array}{cc}3& 6.75\\ 2& 3.50\end{array}\right]\\ =\left[\begin{array}{cc}1.50& 2.25\\ 1.00& 1.75\end{array}\right]\end{array}$

(c)

To determine

To Find: The matrix that shows that the difference in the cost if a child or adult goes after 6:00 PM instead or before 6:00 PM.

Answer to Problem 82SR

The required matrix is $P=\left[\begin{array}{cc}1.00& 1.00\\ 1.50& 1.50\end{array}\right]$ .

Explanation of Solution

Consider matrix that shows that the difference in the cost if a child or adult goes after 6:00 PM instead or before 6:00 PM. Is,

  $P=\left[\begin{array}{cc}1.00& 1.00\\ 1.50& 1.50\end{array}\right]$