Chapter 4, Problem 14SGR

a.

To determine

To describe: The matrix that represent the purchase price of different clothing items.

Answer to Problem 14SGR

The matrix that represent the purchase price of different clothing itemsis

  $\left[\begin{array}{c}15\\ 25\\ 30\end{array}\right]$

Explanation of Solution

Given information:

A table that depicts the purchase price and selling price of shirts, jeans and shoes.

  $\begin{array}{ccc}\text{Item}& \text{Purchase price}& \text{Selling price}\\ \text{shirts}& \$15& \$35\\ \text{jeans}& \$25& \$55\\ \text{shoes}& \$30& \$85\end{array}$

Calculation:

Consider the provided information thata table that depicts the purchase price and selling price of shirts, jeans and shoes.

  $\begin{array}{ccc}\text{Item}& \text{Purchase price}& \text{Selling price}\\ \text{shirts}& \$15& \$35\\ \text{jeans}& \$25& \$55\\ \text{shoes}& \$30& \$85\end{array}$

Denote the three rows of the matrix as three different clothing items and 1 column as purchase price of the items.

Therefore, the matrix that represent the purchase price of different clothing items is provided below,

  $\left[\begin{array}{c}15\\ 25\\ 30\end{array}\right]$

b.

To determine

To describe: The matrix that represent the selling price of different clothing items.

Answer to Problem 14SGR

The matrix that represent the selling price of different clothing items is

  $\left[\begin{array}{c}35\\ 55\\ 85\end{array}\right]$

Explanation of Solution

Given information:

A table that depicts the purchase price and selling price of shirts, jeans and shoes.

  $\begin{array}{ccc}\text{Item}& \text{Purchase price}& \text{Selling price}\\ \text{shirts}& \$15& \$35\\ \text{jeans}& \$25& \$55\\ \text{shoes}& \$30& \$85\end{array}$

Calculation:

Consider the provided information thata table that depicts the purchase price and selling price of shirts, jeans and shoes.

  $\begin{array}{ccc}\text{Item}& \text{Purchase price}& \text{Selling price}\\ \text{shirts}& \$15& \$35\\ \text{jeans}& \$25& \$55\\ \text{shoes}& \$30& \$85\end{array}$

Denote the three rows of the matrix as three different clothing items and 1 column as purchase price of the items.

Therefore, the matrix that represent the selling price of different clothing items is provided below,

  $\left[\begin{array}{c}35\\ 55\\ 85\end{array}\right]$

c.

To determine

To calculate: The profit on single shirt, a pair of jeans and a pair of shoes.

Answer to Problem 14SGR

The profit on single shirt, a pair of jeans and a pair of shoesis

  $\left[\begin{array}{c}20\\ 30\\ 55\end{array}\right]$

Explanation of Solution

Given information:

A table that depicts the purchase price and selling price of shirts, jeans and shoes.

  $\begin{array}{ccc}\text{Item}& \text{Purchase price}& \text{Selling price}\\ \text{shirts}& \$15& \$35\\ \text{jeans}& \$25& \$55\\ \text{shoes}& \$30& \$85\end{array}$

Calculation:

Consider the provided information that a table that depicts the purchase price and selling price of shirts, jeans and shoes.

  $\begin{array}{ccc}\text{Item}& \text{Purchase price}& \text{Selling price}\\ \text{shirts}& \$15& \$35\\ \text{jeans}& \$25& \$55\\ \text{shoes}& \$30& \$85\end{array}$

Denote the three rows of the matrix as three different clothing items and 1 column as purchase price of the items.

Therefore, the matrix that represent the purchase price of different clothing items is provided below,

  $\left[\begin{array}{c}15\\ 25\\ 30\end{array}\right]$

Denote the three rows of the matrix as three different clothing items and 1 column as purchase price of the items.

Therefore, the matrix that represent the selling price of different clothing items is provided below,

  $\left[\begin{array}{c}35\\ 55\\ 85\end{array}\right]$

Profit on each item is the difference between the selling price and purchase price.

  $\left[\begin{array}{c}35\\ 55\\ 85\end{array}\right]-\left[\begin{array}{c}15\\ 25\\ 30\end{array}\right]=\left[\begin{array}{c}20\\ 30\\ 55\end{array}\right]$

Therefore, the profit on single shirt, a pair of jeans and a pair of shoes is

  $\left[\begin{array}{c}20\\ 30\\ 55\end{array}\right]$