During a three-day school fair, a stall sells three types of food – hotdog, mini-pizza and popcorn.

Question

During a three-day school fair, a stall sells three types of food – hotdog, mini-pizza and popcorn. The sales of the items on each day are given in the table below.

	Number of item sold
	Hotdog	Mini-pizza	Popcorn
Day $1$	$32$	$16$	$47$
Day $2$	$48$	$25$	$53$
Day $3$	$25$	$35$	$13$
Cost Price/Item (\$)	$1.50$	$2.00$	$0.50$

The information for the three days' sales can be represented by a $3 \times 3$ matrix $\mathbf{S}$.
Write down matrix $\mathbf{S}$.
The cost price of each item can be represented by a $3 \times 1$ matrix $\mathbf{C}$. Write down matrix $\mathbf{C}$.
1. Evaluate $\mathbf{SC}$.
2. Describe what is represented by the elements of $\mathbf{SC}$.

The profit for the sale of each item as a percentage of the cost price is:

Hotdog	$100\%$
Mini-pizza	$150\%$
Popcorn	$300\%$

The profit from the sale of each item is represented by a matrix $\mathbf{P}$. Write down matrix $\mathbf{P}$.
Given that $\mathbf{R} = \begin{pmatrix} 1 & 1 & 1 \end{pmatrix}$, evaluate $\mathbf{T} = \mathbf{RSP}$ and describe what $\mathbf{T}$ represents.

Accepted Answer

(a) $\begin{pmatrix}32&16&47\48&25&53\25&35&13\end{pmatrix}$; (b) $\begin{pmatrix}1.5\2\0.5\end{pmatrix}$; (c)(i) $\begin{pmatrix}103.5\148.5\114\end{pmatrix}$; (ii) daily cost totals in dollars; (d) $\begin{pmatrix}1.5\3\1.5\end{pmatrix}$; (e) $\begin{pmatrix}555\end{pmatrix}$, total three-day profit in dollars.

	Number of item sold
	Hotdog	Mini-pizza	Popcorn
Day \(1\)	\(32\)	\(16\)	\(47\)
Day \(2\)	\(48\)	\(25\)	\(53\)
Day \(3\)	\(25\)	\(35\)	\(13\)
Cost Price/Item (\$)	\(1.50\)	\(2.00\)	\(0.50\)

Matrices - Application of Matrices

Matrices - Application of Matrices

Solution:

Solution locked

Hotdog	\(100\%\)
Mini-pizza	\(150\%\)
Popcorn	\(300\%\)