Question

Two manufacturers Ram and Shyam manufacture only three wooden items; bed, table and sofa. The sales (in rupees) of these three items by both of manufacturers in months of June and July are given by the following matrices $A$ and $B$ respectively.

Sale in June
$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}A=\left[\begin{array}{ccc}5000& 10000& 15000\\ 25000& 15000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

Sale in July
$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}B=\left[\begin{array}{ccc}2500& 5000& 3000\\ 10000& 5000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

The combined sales in June and July for each manufacturer in each item is given by

[2 marks]

• A. $\begin{array}{ccccc}& \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\left[\begin{array}{ccc}15000& 30000& 36000\\ 70000& 40000& 20000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$
• B. $\begin{array}{ccccc}& \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\left[\begin{array}{ccc}7500& 15000& 18000\\ 35000& 20000& 10000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$
• C. $\begin{array}{ccccc}& \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\left[\begin{array}{ccc}75000& 18000& 15000\\ 35000& 10000& 20000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$
• D. $\begin{array}{ccccc}& \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\left[\begin{array}{ccc}75000& 18000& 10000\\ 35000& 20000& 18000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

Answer 1

The correct option is B $\begin{array}{ccccc}& \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\left[\begin{array}{ccc}7500& 15000& 18000\\ 35000& 20000& 10000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

Combined sales in June and July for each manufacture in each item is
$\begin{array}{ccccccccc}& & & & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}A+B=\left[\begin{array}{ccc}5000& 10000& 15000\\ 25000& 15000& 5000\end{array}\right]+\begin{array}{ccccc}& \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\left[\begin{array}{ccc}2500& 5000& 3000\\ 10000& 5000& 5000\end{array}\right]$

$\begin{array}{cccccccccc}& & & & & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}\Rightarrow A+B=\left[\begin{array}{ccc}7500& 15000& 18000\\ 35000& 20000& 10000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$