set up matrix

**tukeywilliams** · July 31st 2007, 11:42 AM

So we have $S = \begin{bmatrix} 60 & 40 & 25 \\ 80 & 123 & 90 \\ 10 & 0 & 25 \end{bmatrix}$ and

$P = \begin{bmatrix} 1 & 1 & 1.50 \\ 5 & 8 & 6 \\ 20 & 25 & 30 \end{bmatrix}$

Then $P^T = \begin{bmatrix} 1 & 5 & 20 \\ 1 & 8 & 25 \\ 1.50 & 6 & 30 \end{bmatrix}$

So $A = \begin{bmatrix} 1 & 1 & 1.50 \\ 5 & 8 & 6 \\ 20 & 25 & 30 \end{bmatrix}\begin{bmatrix} 1 & 5 & 20 \\ 1 & 8 & 25 \\ 1.50 & 6 & 30 \end{bmatrix} = \begin{bmatrix} 4.25 & 22& 90 \\ 22 & 125 & 480 \\ 90 & 480 & 1925 \end{bmatrix}$

$S^T = \begin{bmatrix} 60 & 80 & 10 \\ 40 & 123 & 0 \\ 25 & 90 & 25 \end{bmatrix}$

Then $B = \begin{bmatrix} 60 & 80 & 10 \\ 40 & 123 & 0 \\ 25 & 90 & 25 \end{bmatrix}\begin{bmatrix} 1 & 1 & 1.50 \\ 5 & 8 & 6 \\ 20 & 25 & 30 \end{bmatrix} = \begin{bmatrix} 660 & 950 & 870 \\655 & 1024 &798 \\ 975 & 1370 & 1327.5 \end{bmatrix}$

So $a_{11} = 4.25$ which is the money made on t-shirts and $b_{33} = 1327.5$ is the money made on tennis rackets.

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