Question

A manufacturer sells the products x,y,z in two markets, annual sales are indicated below.
$\begin{array}{cccc}Market& Products& & \\ I& 10000& 2000& 18000\\ II& 6000& 20000& 8000\end{array}$
(b)If the unit costs of the above three commodities are Rs 2.00m Rs 1.00 and 50 paise respectively. Find the gross profit.

Answer 1

The matrix representing the cost price per unit is $C=\left[\begin{array}{c}2.00\\ 1.00\\ 0.50\end{array}\right]$
$\therefore$ Total cost in the two markets is given by the product
$AC=\left[\begin{array}{ccc}10000& 2000& 18000\\ 6000& 20000& 8000\end{array}\right]\left[\begin{array}{c}2\\ 1\\ \frac{1}{2}\end{array}\right]AC=\left[\begin{array}{c}10000\times 2+2000\times 1+18000\times \frac{1}{2}\\ 6000\times 2+20000\times 1+8000\times \frac{1}{2}\end{array}\right]=\left[\begin{array}{c}31000\\ 36000\end{array}\right]$
Profit in market I=Rs(46000-31000)=Rs 15000
and profit in market II=Rs(53000-36000)=Rs 17000
$\therefore$ The gross profit =Rs (15000+17000)=Rs 32000.