Market | Products | ||
I | 10000 | 2000 | 18000 |
II | 6000 | 20000 | 8000 |
(a) The unit sale prices of \(x, y\), and \(z\) are respectively given as Rs 2.50, Rs 1.50, and Rs 1.00. Consequently, the total revenue in market I can be represented in the form of a matrix as:
\(\begin{bmatrix}10000& 2000& 18000\end{bmatrix}\begin{bmatrix}2.50\\ 1.50\\ 1.00\end{bmatrix}\)
\(=10000\times2.50+2000\times1.50+18000\times1.00]\)
\(=25000+3000+18000\)
\(=46000\)
The total revenue in market II can be represented in the form of a matrix as:
\(\begin{bmatrix}6000& 20000& 8000\end{bmatrix}\begin{bmatrix}2.50\\ 1.50\\ 1.00\end{bmatrix}\)
\(=6000\times2.50+20000\times1.50+8000\times1.00\)
\(=15000+30000+8000\)
\(=53000\)
Therefore, the total revenue in market I is Rs 46000 and the same in market II is Rs 53000.
(b) The unit cost prices of x, y, and z are respectively given as Rs 2.00, Rs 1.00, and 50 paise.
Consequently, the total cost prices of all the products in market I can be represented in the form of a matrix as:
\(\begin{bmatrix}10000& 2000& 18000\end{bmatrix}\begin{bmatrix}2.00\\ 1.00\\ 0.50\end{bmatrix}\)
\(=10000\times2.00+2000\times1.00+18000\times0.50\)
\(=20000+2000+9000\)
\(=31000\)
Since the total revenue in market I is Rs 46000, the gross profit in this market is (Rs 46000−Rs 31000) Rs 15000.
The total cost prices of all the products in market II can be represented in the form of a matrix as:
\(\begin{bmatrix}6000& 20000& 8000\end{bmatrix}\begin{bmatrix}2.00\\ 1.00\\ 0.50\end{bmatrix}\)
\(=6000\times2.00+20000\times1.00+8000\times0.50\)
\(=12000+20000+4000\)
\(=Rs 36000\)
Since the total revenue in market II isRs 53000, the gross profit in this market is (Rs53000 − Rs 36000) Rs 17000.