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# A manufacturer produces three products $$x, y, z$$ which he sells in two markets. Annual sales are indicated below: $\begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array}$ If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market

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• If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
step 1: (a)Matrix for the products x,y,z is $\begin{array} { c c } x & y & z \\ 10,000 & 2,000 & 18,000 \\ 6,000 & 20,000 & 8,000 \end{array}$
Matrix corresponding to sale price of each product$\begin{array}{1 1}x\\y\\z\end{array}\begin{bmatrix}2.50\\1.50\\1.00\end{bmatrix}$
The revenue collected by the market is given by$\begin{bmatrix}10000 & 2000 & 18000\\6000 & 20000 & 8000\end{bmatrix}\begin{bmatrix}2.50\\1.50\\1.00\end{bmatrix}$
Step 2: Multiply each row with the column
$\begin{bmatrix}25000+3000+18000\\15000+30000+8000\end{bmatrix}$
$\begin{bmatrix}46000\\53000\end{bmatrix}$
Thus Revenue in each market is Rs 46000 and 53000.
Total Revenue=46000+53000=Rs 99000
edited Mar 19, 2013