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  • 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,

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.

Answers (1)

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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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