A fruit juice stall sells regular, medium and large glasses of apple and orange juice. The number of glasses of each type of juice that was sold on a particular morning are summarised in the following table.

Regular (R)	Medium (M)	Large (L)
Apple Juice	20	30
Orange Juice	14	36

1. Place the table values into the matrix in the correct row and column order.

The rows are Apple Juice and Orange Juice, and the columns are Regular, Medium and Large.

So
$J=\begin{pmatrix}20&30&11\\14&36&8\end{pmatrix}$

1. Set up the matrix product using the rows of $J$ and the column of $C$.

Using $J=\begin{pmatrix}20&30&11\\14&36&8\end{pmatrix},\quad C=\begin{pmatrix}1.5\\2\\3\end{pmatrix},$
$M=JC=\begin{pmatrix}20&30&11\\14&36&8\end{pmatrix}\begin{pmatrix}1.5\\2\\3\end{pmatrix}.$

2. Perform row-by-column multiplication and simplify each element.

$M=\begin{pmatrix}20(1.5)+30(2)+11(3)\\14(1.5)+36(2)+8(3)\end{pmatrix}$
$=\begin{pmatrix}30+60+33\\21+72+24\end{pmatrix}$
$=\begin{pmatrix}123\\117\end{pmatrix}.$

1. Interpret each element of $M$ in context.

Since
$M=JC=\begin{pmatrix}123\\117\end{pmatrix},$
the first row corresponds to apple juice and the second row corresponds to orange juice.

Therefore, $123$ is the total cost price of the apple juice sold, and $117$ is the total cost price of the orange juice sold.

1. Find the selling price of each glass size and form the price matrix.

Profit is $80\%$ of cost price, so
$\text{selling price}=100\%+80\%=180\%\text{ of cost price}.$

Thus the selling-price matrix is
$1.8C=1.8\begin{pmatrix}1.5\\2\\3\end{pmatrix}=\begin{pmatrix}2.70\\3.60\\5.40\end{pmatrix}.$

2. Set up and evaluate the matrix product for the total sales.

Using
$J=\begin{pmatrix}20&30&11\\14&36&8\end{pmatrix},$

$J(1.8C)=\begin{pmatrix}20&30&11\\14&36&8\end{pmatrix}\begin{pmatrix}2.70\\3.60\\5.40\end{pmatrix}.$

3. Carry out row-by-column multiplication and state the total sales.

So
$J(1.8C)=\begin{pmatrix}221.40\\210.60\end{pmatrix}.$