The table below shows the number of tubs of ice cream of four different brands: $A$, $B$, $C$

Question

The table below shows the number of tubs of ice cream of four different brands: $A$, $B$, $C$ and $D$, sold at $3$ dessert shops.

	Brand $A$	Brand $B$	Brand $C$	Brand $D$
Shop $1$	$5$	$3$	$1$	$1$
Shop $2$	$11$	$6$	$8$	$5$
Shop $3$	$8$	$5$	$4$	$3$

A tub of ice cream costs $\$15$ for Brand $A$, $\$10$ for Brand $B$, $\$8$ for Brand $C$ and $\$5$ for Brand $D$.

Given the matrix $P = \begin{pmatrix} 15 \\ 10 \\ 8 \\ 5 \end{pmatrix}$,

1. Write down a $3 \times 4$ matrix $Q$ that represents the data in the table above.
2. Evaluate $QP$.
3. Explain what the elements in $QP$ represent.

Brand $A$ comes in tubs of $180$ g, Brand $B$ in tubs of $200$ g, Brand $C$ in tubs of $150$ g and Brand $D$ in tubs of $100$ g.

1. Write down a matrix $S$, such that matrix $QS$ represents the total number of grams of ice cream sold by each shop.
2. Evaluate $QS$.
3. Using matrix multiplication, find the total number of grams of ice cream sold by the $3$ shops.

Accepted Answer

(a)(i) $\begin{pmatrix}5&3&1&1\11&6&8&5\8&5&4&3\end{pmatrix}$; (ii) $\begin{pmatrix}118\314\217\end{pmatrix}$; (iii) sales values in dollars for Shops 1, 2 and 3. (b)(i) $\begin{pmatrix}180\200\150\100\end{pmatrix}$; (ii) $\begin{pmatrix}1750\4880\3340\end{pmatrix}$ g; (iii) 9970 g.

	Brand \(A\)	Brand \(B\)	Brand \(C\)	Brand \(D\)
Shop \(1\)	\(5\)	\(3\)	\(1\)	\(1\)
Shop \(2\)	\(11\)	\(6\)	\(8\)	\(5\)
Shop \(3\)	\(8\)	\(5\)	\(4\)	\(3\)

Mathematical Modeling for Inventory Management

Mathematical Modeling for Inventory Management

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