Question

For Exercises 40-42, use the table below that shows the purchase price and selling price of stock for three companies.

For a class project, Taini “bought: shares of stock in three companies. She bought 150 shares of a utility company, 100 shares of a computer company, and 200 shares of a food company. At the end of the project she “sold” all of her stock.

Use matrix operations to find how much money Taini “made” or “lost”?

Short answer

The money has been made that is$1460$ .

Step-by-step solution

Step 1- Write the required matrices 

Form the matrices according to the provided information.

$S=\left[\begin{array}{ccc}150& 100& 200\end{array}\right]$

$P=\left[\begin{array}{cc}54& 55.20\\ 48& 58.60\\ 60& 61.10\end{array}\right]$

– Write the product of obtained matrices

Perform multiplication between the matrices $S=\left[\begin{array}{ccc}150& 100& 200\end{array}\right]$and

$P=\left[\begin{array}{cc}54& 55.20\\ 48& 58.60\\ 60& 61.10\end{array}\right]$

$\begin{array}{c}SP=\left[\begin{array}{ccc}150& 100& 200\end{array}\right]\cdot \left[\begin{array}{cc}54& 55.20\\ 48& 58.60\\ 60& 61.10\end{array}\right]\\ =\left[\begin{array}{cc}24900& 26360\end{array}\right]\end{array}$

Step 3- Observe the obtained matrix

The first column of the obtained matrix is related to purchase and second is related to sell. As the amount of selling is higher than the purchasing so it indicate towards that the money has been made.

Step 4- Make the conclusion

The difference between 24900 and 26360 provides the amount of the profit that is $26360-24900=1460$.