On every weekday, a bakery delivers chicken pies and apple pies to four cafes. On every weekend, it delivers double the number of chicken pies and apple pies to each of the cafe. The matrix E shows the number of chicken and apple pies delivered to each cafe on each weekday and each weekend

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.

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