Chapter 12.1, Problem 23PPE

To determine

To check: that which of the factory made more chairs during both shifts by using matrices.

Answer to Problem 23PPE

Factory B.

Explanation of Solution

Given:

During the first shift, Factory A made 250 chairs and 145 tables and Factory B made 300 chairs and 75 tables.

During the second shift, Factory A made 275 chairs and 90 tables and Factory B made 240 chairs and 120 tables.

Calculation:

According to the question

First create a matrix for the first shift with the top row being factory A and the bottom row being Factory B and with the left column being number of chairs made and the right column being number of tables and fill in the corresponding numbers.

  $\left[\begin{array}{l}250145\\ 30075\end{array}\right]$

Then create a matrix for the second shift with the top row being factory A and the bottom row being Factory B and with the left column being number of chairs made and the right column being number of tables and fill in the corresponding numbers.

  $\left[\begin{array}{l}27590\\ 240120\end{array}\right]$

Now, add the matrices, then

  $\left[\begin{array}{l}250145\\ 30075\end{array}\right]+\left[\begin{array}{l}27590\\ 240120\end{array}\right]=\left[\begin{array}{l}525235\\ 540195\end{array}\right]$

Compare the top left value in the matrix (number of chairs factory A made over 2 shifts) to the bottom left value in the matrix (number of chairs factory B made over 2 shifts).

  $525<540$

Hence, Factory B produced more chair.