Chapter 3, Problem 33SGR

(a)

To determine

To write: Matrix for the purchase price.

Answer to Problem 33SGR

Matrix for the purchase price:

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

Explanation of Solution

Given information:

Table for the purchase price and the selling price:

Items	Purchase Price	Selling Price
shirts	$15	$35
jeans	$25	$55
shoes	$30	$85

From the table,

Purchase price for 1 shirt is $15.

Purchase price for 1 pair of jeans is $25.

Purchase price for 1 pair of shoes is $30.

Thus,

The matrix becomes

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

(b)

To determine

To write: Matrix for the selling price.

Answer to Problem 33SGR

Matrix for the selling price:

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

Explanation of Solution

Given information:

Table for the purchase price and the selling price:

Items	Purchase Price	Selling Price
shirts	$15	$35
jeans	$25	$55
shoes	$30	$85

From the table,

Selling price for 1 shirt is $35.

Selling price for 1 pair of jeans is $55.

Selling price for 1 pair of shoes is $85.

Thus,

The matrix becomes

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

(c)

To determine

To write: Matrix for profit on 1 shirt, 1 pair of jeans, and 1 pair of shoes.

Answer to Problem 33SGR

Profit Matrix:

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

Explanation of Solution

Given information:

Table for the purchase price and the selling price:

Items	Purchase Price	Selling Price
shirts	$15	$35
jeans	$25	$55
shoes	$30	$85

Difference between the selling price and purchase price:

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

Subtract the corresponding values:

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

Simplify:

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

Thus,

The matrix for profit:

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