在每个工作日，一家面包店向四家咖啡馆配送鸡肉派和苹果派。在每个周末，它向每家咖啡馆配送双倍数量的鸡肉派和苹果派。 矩阵 E 显示了每个工作日和每个周末配送到每家咖啡馆的鸡肉派和苹果派的数量

1. Multiply every entry of $E$ by $4$.

$M=4E=4\begin{pmatrix}38&50\\76&100\end{pmatrix}=\begin{pmatrix}4(38)&4(50)\\4(76)&4(100)\end{pmatrix}=\begin{pmatrix}152&200\\304&400\end{pmatrix}$

1. Multiply the row matrix by each column of \(M\).

From part (a),
$M=\begin{pmatrix}152&200\\304&400\end{pmatrix}.$

1. Identify what the row multiplier represents and interpret each element of $C$.

Since $M$ gives the numbers of pies delivered to the $4$ cafes on one weekday and one weekend day, multiplying by $\begin{pmatrix}5&2\end{pmatrix}$ gives
$5(\text{weekday deliveries})+2(\text{weekend deliveries}).$
Therefore,
$C=\begin{pmatrix}1368&1800\end{pmatrix}$
represents the total numbers delivered in one week: $1368$ chicken pies and $1800$ apple pies.

1. Form the matrix multiplication using weekly quantities and prices.

From part (b),
$C=\begin{pmatrix}1368&1800\end{pmatrix}$
The price matrix is
$\begin{pmatrix}1.80\\1.50\end{pmatrix}$
So the total amount collected is
$\begin{pmatrix}1368&1800\end{pmatrix}\begin{pmatrix}1.80\\1.50\end{pmatrix}$

2. Evaluate the matrix product to find the total weekly collection.

$1368(1.80)+1800(1.50)=2462.40+2700=5162.40$