# Q10.    A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below:                Market                                       Products                     I                                10,000    2,000    18,000                    II                                6,000      20,000    8,000            (a) If unit sale prices of x, y and z are  2.50,  1.50 and  1.00, respectively, find the total revenue in each market with the help of matrix algebra.

The unit sale prices of x, y and z are  2.50,  1.50 and  1.00, respectively.

The total revenue in the market I with the help of matrix algebra can be represented as :

$\begin{bmatrix} 10000& 2000 & 18000 \end{bmatrix} \begin{bmatrix} 2.50\\ 1.50\\ 1.00 \end{bmatrix}$

$= 10000\times 2.50+2000\times 1.50+18000\times 1.00$

$= 25000+3000+18000$

$= 46000$

The total revenue in market II with the help of matrix algebra can be represented as :

$\begin{bmatrix} 6000& 20000 & 8000 \end{bmatrix} \begin{bmatrix} 2.50\\ 1.50\\ 1.00 \end{bmatrix}$

$= 6000\times 2.50+20000\times 1.50+8000\times 1.00$

$= 15000+30000+8000$

$= 53000$

Hence, total revenue in the market I is 46000 and total revenue in market II is 53000.

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