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

If both manufacturers receive $2\%$ profit on gross sale, then profit of both manufacturers for each item in July is given by

[2 marks]

• A. $\begin{array}{cc}\text{Bed}\text{Table}\text{Sofa}& \end{array}\left[\begin{array}{ccc}50& 100& 60\\ 200& 100& 50\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$
• B. $\begin{array}{cc}\text{Bed}\text{Table}\text{Sofa}& \end{array}\left[\begin{array}{ccc}50& 100& 60\\ 100& 100& 100\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$
• C. $\begin{array}{cc}\text{Bed}\text{Table}\text{Sofa}& \end{array}\left[\begin{array}{ccc}50& 100& 60\\ 200& 100& 100\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$
• D. $\begin{array}{cc}\text{Bed}\text{Table}\text{Sofa}& \end{array}\left[\begin{array}{ccc}50& 100& 60\\ 200& 50& 100\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

Answer 1

The correct option is C $\begin{array}{cc}\text{Bed}\text{Table}\text{Sofa}& \end{array}\left[\begin{array}{ccc}50& 100& 60\\ 200& 100& 100\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

Profit of both manufacturers for each item in July is
$2\%$ of $B$
$=\frac{2}{100}\times B$
$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}=\frac{1}{50}\left[\begin{array}{ccc}2500& 5000& 3000\\ 10000& 5000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$

$\begin{array}{ccc}& \text{Bed}\text{Table}\text{Sofa}& \end{array}=\left[\begin{array}{ccc}50& 100& 60\\ 200& 100& 100\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$