Using Matrices in Real-World Problems

Let’s return to the problem presented at the opening of this section. We have the table, representing the equipment needs of two soccer teams.

$$\begin{array}{ccc}& \text{Wildcats}& \text{Mud Cats}\\ \text{Goals}& \text{6}& \text{10}\\ \text{Balls}& \text{30}& \text{24}\\ \text{Jerseys}& \text{14}& \text{20}\end{array}$$
We are also given the prices of the equipment, as shown in the table.

\begin{array}{|c|c|}\hline \text{Goal} & \text{$300} \\ \hline \text{Ball} & \text{$10} \\ \hline \text{Jersey} & \text{$30} \\ \hline\end{array}
We will convert the data to matrices. Thus, the equipment need matrix is written as

$$E=\left[\begin{array}{c}6\\ 30\\ 1410\\ 24\\ 20\end{array}\right]$$

The cost matrix is written as

$$C=\left[\begin{array}{ccc}300& 10& 30\end{array}\right]$$

We perform matrix multiplication to obtain costs for the equipment.

$$\begin{array}{c}\\ \\ CE=\left[\begin{array}{c}\begin{array}{ccc}300& 10& 30\end{array}\end{array}\right]\left[\begin{array}{c}\begin{array}{cc}6& 10\\ 30& 24\\ 14& 20\end{array}\end{array}\right]\\ =\left[\begin{array}{c}\begin{array}{cc}300\left(6\right)+10\left(30\right)+30\left(14\right)& 300\left(10\right)+10\left(24\right)+30\left(20\right)\end{array}\end{array}\right]\\ =\left[\begin{array}{c}\begin{array}{cc}2,520& 3,840\end{array}\end{array}\right]\end{array}$$

The total cost for equipment for the Wildcats is $2,520, and the total cost for equipment for the Mud Cats is $3,840.

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Algebra and Trigonometry 2e · §11.5 Matrices and Matrix Operations · Example 12