一家蛋糕店销售3种蛋糕。
第1天，该店售出了84个巧克力蛋糕、90个香草蛋糕和56个草莓蛋糕。
第2天，该店售出了92个巧克力蛋糕、60个香草蛋糕和61个草莓蛋糕。

1. Place the given sales data into a $2\times 3$ matrix in the correct order.

Use rows for Day 1 and Day 2, and columns for Chocolate, Vanilla and Strawberry.

$P=\begin{pmatrix}84&90&56\\92&60&61\end{pmatrix}$

1. Multiply the $2\times3$ sales matrix by the $3\times2$ price-and-profit matrix.

Using $P=\begin{pmatrix}84&90&56\\92&60&61\end{pmatrix},$

$$R=\begin{pmatrix}84&90&56\\92&60&61\end{pmatrix} \begin{pmatrix}7&4\\8&3\\9&5\end{pmatrix}$$ $$=\begin{pmatrix} 84(7)+90(8)+56(9) & 84(4)+90(3)+56(5)\\ 92(7)+60(8)+61(9) & 92(4)+60(3)+61(5) \end{pmatrix}$$ $$=\begin{pmatrix} 1812&886\\ 1691&859 \end{pmatrix}.$$

1. Calculate the profit for Day 1 as a percentage of the total sale for Day 1.

From part (b), for Day 1,

Total sale $=1812$, profit $=886$.

$\frac{886}{1812}\times 100\%=48.896\ldots\%$

$\approx 48.9\%$

1. Substitute the matrix $R$ and carry out the row-by-matrix multiplication, then multiply by $\frac12$.

From part (b),
$R=\begin{pmatrix}1812&886\\1691&859\end{pmatrix}.$

$M=\frac12(1\;1)\begin{pmatrix}1812&886\\1691&859\end{pmatrix}$

$=\frac12\begin{pmatrix}1812+1691&886+859\end{pmatrix}$

$=\frac12\begin{pmatrix}3503&1745\end{pmatrix}$

$=\begin{pmatrix}1751.5&872.5\end{pmatrix}$

1. Interpret the two elements of $M$ from the columns of $R$.

In $R=\begin{pmatrix}1812&886\\1691&859\end{pmatrix}$, the first column represents total sales and the second column represents total profits for the two days.

Since
$M=\frac12(1\;1)R=\begin{pmatrix}1751.5&872.5\end{pmatrix},$
$M$ gives the average of the two days for each column.

So $1751.5$ is the average daily total sale, and $872.5$ is the average daily profit.