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A manufacturer produces three products $x,\, y,\, z$ which he sells in two markets. Annual sales are indicated below:
| Market | $x$ | $y$ | $z$ |
| $I$ | $10,000$ | $2,000$ | $18,000$ |
| $II$ | $6,000$ | $20,000$ | $8,000$ |
If the unit costs of the above three commodities are $\mathrm{Rs} $. $2.00, $ $\mathrm{Rs} $. $1.00$ and $50$ paise respectively. Find the gross profit.
$32,000$
$32,000$
$32,000$
$32,000$
Solution
The unit cost price of $x,\,y$ and $z$ are respectively given as $\mathrm{Rs}.\, 2.00 $ $\mathrm{Rs}. \,1.00$ and $50$ paise.
Consequently, the total cost prices of all the products in the market I can be represented in the form of a matrix as :
$\left[\begin{array}{lll}10000 & 2000 & 18000\end{array}\right]\left[\begin{array}{l}2.50 \\ 1.00 \\ 0.50\end{array}\right]$
$=10000 \times 2.00+2000 \times 1.00+18000 \times 0.50$
$=20000+2000+9000=31000$
since the total revenue in market $\mathrm{I}$ is $ \mathrm{Rs}\, 46000,$ the gross profit in this market is $\mathrm{Rs}.\, 46000- \mathrm{Rs}. \,31000=\mathrm{Rs}. \,15000$
The total cost prices of all the products in market $II$ can be represented in the form of a matrix as:
$\left[\begin{array}{lll}6000 & 20000 & 8000\end{array}\right]\left[\begin{array}{l}2.00 \\ 1.00 \\ 0.50\end{array}\right]$
$=6000 \times 2.00+20000 \times 1.00+8000 \times 0.50$
$=12000+20000+4000$
$=36000$
since the total revenue in market $\mathrm{I} \mathrm{I}$ is $\mathrm{Rs} 53000,$ the gross profit in this market is $ \mathrm{Rs}.$ $53000-$ $ \mathrm{Rs}.$ $36000=$ $ \mathrm{Rs}. \,17000$.
