A retailer sells Notebooks and Pens at two shops. Shop I sold 50 Notebooks and 80 Pens; Shop II sold 40 Notebooks and 60 Pens. If a Notebook costs Rs 20 and a Pen costs Rs 5, use matrix multiplication to find the total sales revenue at each shop.

Question

Accepted Answer

**Step 1 — Set up the quantity matrix and the cost matrix**

Let row 1 = Shop I, row 2 = Shop II, column 1 = Notebooks, column 2 = Pens:
$$Q=\begin{pmatrix}50&80\40&60\end{pmatrix},\qquad C=\begin{pmatrix}20\5\end{pmatrix}$$

$Q$ is $2	imes2$ and $C$ is $2	imes1$, so $QC$ is defined and will be $2	imes1$ — one total-revenue figure per shop.

**Step 2 — Compute $QC$ by the row-by-column rule**

$$QC=\begin{pmatrix}50(20)+80(5)\40(20)+60(5)\end{pmatrix}=\begin{pmatrix}1000+400\800+300\end{pmatrix}=\begin{pmatrix}1400\1100\end{pmatrix}$$

So Shop I's total revenue is Rs 1,400 and Shop II's total revenue is Rs 1,100. …

Q.A retailer sells Notebooks and Pens at two shops. Shop I sold 50 Notebooks and 80 Pens; Shop II sold 40 Notebooks and 60 Pens. If a Notebook costs Rs 20 and a Pen costs Rs 5, use matrix multiplication to find the total sales revenue at each shop.

Concept understanding — Matrix Algebra: Addition, Subtraction and Multiplication

Q.A retailer sells Notebooks and Pens at two shops. Shop I sold 50 Notebooks and 80 Pens; Shop II sold 40 Notebooks and 60 Pens. If a Notebook costs Rs 20 and a Pen costs Rs 5, use matrix multiplication to find the total sales revenue at each shop.

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