Chapter MPS, Problem 4.2MPS

a.

To determine

Organize the data in matrix

Answer to Problem 4.2MPS

  $C=\left[\begin{array}{ccc}582& 132& 85\\ 621& 129& 89\\ 594& 131& 95\end{array}\right]$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

The matrix which represents the current price is as follows.

  $C=\left[\begin{array}{ccc}582& 132& 85\\ 621& 129& 89\\ 594& 131& 95\end{array}\right]$

b.

To determine

Find the scalar value for price.

Answer to Problem 4.2MPS

  $0.25$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

Hence, the scaler which determine the new prices is $0.25$ .

c.

To determine

Find the $N$ .

Answer to Problem 4.2MPS

  $=\left[\begin{array}{ccc}145.5& 33& 21.25\\ 155.25& 32.25& 22.25\\ 148.5& 32.75& 23.75\end{array}\right]$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

The matrix which represents the new price is as follows.

  $\begin{array}{l}N=0.25\left[\begin{array}{ccc}582& 132& 85\\ 621& 129& 89\\ 594& 131& 95\end{array}\right]\\ =\left[\begin{array}{ccc}145.5& 33& 21.25\\ 155.25& 32.25& 22.25\\ 148.5& 32.75& 23.75\end{array}\right]\end{array}$

d.

To determine

Find the value of N-C.

Answer to Problem 4.2MPS

  $-\left[\begin{array}{ccc}436.5& 99& 63.75\\ 465.75& 96.75& 66.75\\ 445.5& 98.25& 71.25\end{array}\right]$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Store& Television& \begin{array}{l}DVD\\ Player\end{array}& \begin{array}{l}CD\\ Player\end{array}\\ 1& 582& 132& 85\\ 2& 621& 129& 89\\ 3& 594& 131& 95\end{array}$

The value is calculated below.

  $\begin{array}{l}N-C=\left[\begin{array}{ccc}145.5& 33& 21.25\\ 155.25& 32.25& 22.25\\ 148.5& 32.75& 23.75\end{array}\right]-\left[\begin{array}{ccc}582& 132& 85\\ 621& 129& 89\\ 594& 131& 95\end{array}\right]\\ =\left[\begin{array}{ccc}-436.5& -99& -63.75\\ -465.75& -96.75& -66.75\\ -445.5& -98.25& -71.25\end{array}\right]\\ =-\left[\begin{array}{ccc}436.5& 99& 63.75\\ 465.75& 96.75& 66.75\\ 445.5& 98.25& 71.25\end{array}\right]\end{array}$

Hence, the value is $-\left[\begin{array}{ccc}436.5& 99& 63.75\\ 465.75& 96.75& 66.75\\ 445.5& 98.25& 71.25\end{array}\right]$ .