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Question

(A) Let the sales matrix be $A = \begin{bmatrix} 10000 & 2000 & 18000 \ 6000 & 20000 & 8000 \end{bmatrix}$.Let the unit sale price matrix be $S = \be

Vedclass · Accepted Answer

$32000$

Vedclass · Answer

(A) Let the sales matrix be $A = \begin{bmatrix} 10000 & 2000 & 18000 \ 6000 & 20000 & 8000 \end{bmatrix}$.Let the unit sale price matrix be $S = \begin{bmatrix} 2.50 \ 1.50 \ 1.00 \end{bmatrix}$ and unit cost price matrix be $C = \begin{bmatrix} 2.00 \ 1.00 \ 0.50 \end{bmatrix}$.Profit per unit is $P = S - C = \begin{bmatrix} 2.50-2.00 \ 1.50-1.00 \ 1.00-0.50 \end{bmatrix} = \begin{bmatrix} 0.50 \ 0.50 \ 0.50 \end{bmatrix}$.Total profit is given by the matrix product $A 	imes P$:$\begin{bmatrix} 10000 & 2000 & 18000 \ 6000 & 20000 & 8000 \end{bmatrix} \begin{bmatrix} 0.50 \ 0.50 \ 0.50 \end{bmatrix} = \begin{bmatrix} 10000(0.50) + 2000(0.50) + 18000(0.50) \ 6000(0.50) + 20000(0.50) + 8000(0.50) \end{bmatrix}$$= \begin{bmatrix} 5000 + 1000 + 9000 \ 3000 + 10000 + 4000 \end{bmatrix} = \begin{bmatrix} 15000 \ 17000 \end{bmatrix}$.Total gross profit = $15000 + 17000 = 32000$.

Market	$x$	$y$	$z$
$I$	$10,000$	$2,000$	$18,000$
$II$	$6,000$	$20,000$	$8,000$

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