Question 133
Multiple Choice The following tables give annual production costs and profits at Gauss Jordan Sneakers. Production costs 2001 2002 2003 Gauss Grip $ 1 , 100 $ 2 , 700 $ 3 , 500 Air Gauss $ 1 , 000 $ 1 , 800 $ 2 , 900 Gauss Gel $ 1 , 900 $ 2 , 800 $ 1 , 200 Profits 2001 2002 2003 Gauss Grip $ 17 , 000 $ 13 , 000 $ 24 , 000 Air Gauss $ 8 , 000 $ 16 , 000 $ 13 , 000 Gauss Gel $ 6 , 000 $ 12 , 000 $ 20 , 000 \begin{array}{l}\begin{array} { | l | l | l | l | } \hline \text { Production costs } & \mathbf { 2 0 0 1 } & \mathbf { 2 0 0 2 } & \mathbf { 2 0 0 3 } \\\hline \text { Gauss Grip } & \$ 1,100 & \$ 2,700 & \$ 3,500 \\\hline \text { Air Gauss } & \$ 1,000 & \$ 1,800 & \$ 2,900 \\\hline \text { Gauss Gel } & \$ 1,900 & \$ 2,800 & \$ 1,200 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | } \hline \text { Profits } & \mathbf { 2 0 0 1 } & \mathbf { 2 0 0 2 } & \mathbf { 2 0 0 3 } \\\hline \text { Gauss Grip } & \$ 17,000 & \$ 13,000 & \$ 24,000 \\\hline \text { Air Gauss } & \$ 8,000 & \$ 16,000 & \$ 13,000 \\\hline \text { Gauss Gel } & \$ 6,000 & \$ 12,000 & \$ 20,000 \\\hline\end{array}\end{array} Production costs Gauss Grip Air Gauss Gauss Gel 2001 $1 , 100 $1 , 000 $1 , 900 2002 $2 , 700 $1 , 800 $2 , 800 2003 $3 , 500 $2 , 900 $1 , 200 Profits Gauss Grip Air Gauss Gauss Gel 2001 $17 , 000 $8 , 000 $6 , 000 2002 $13 , 000 $16 , 000 $12 , 000 2003 $24 , 000 $13 , 000 $20 , 000 Write the matrix algebraic formula to compute the revenues from each sector each year.
A) [ 1 , 100 2 , 700 3 , 500 1 , 000 1 , 800 2 , 900 1 , 900 2 , 800 1 , 200 ] + [ 15 , 900 10 , 300 20 , 500 7 , 000 14 , 200 10 , 100 4 , 100 9 , 200 18 , 800 ] = [ 17 , 000 13 , 000 24 , 000 8 , 000 16 , 000 13 , 000 6 , 000 12 , 000 20 , 000 ] \left[ \begin{array} { l l l } 1,100 & 2,700 & 3,500 \\1,000 & 1,800 & 2,900 \\1,900 & 2,800 & 1,200\end{array} \right] + \left[ \begin{array} { c c c } 15,900 & 10,300 & 20,500 \\7,000 & 14,200 & 10,100 \\4,100 & 9,200 & 18,800\end{array} \right] = \left[ \begin{array} { c c c } 17,000 & 13,000 & 24,000 \\8,000 & 16,000 & 13,000 \\6,000 & 12,000 & 20,000\end{array} \right] 1 , 100 1 , 000 1 , 900 2 , 700 1 , 800 2 , 800 3 , 500 2 , 900 1 , 200 + 15 , 900 7 , 000 4 , 100 10 , 300 14 , 200 9 , 200 20 , 500 10 , 100 18 , 800 = 17 , 000 8 , 000 6 , 000 13 , 000 16 , 000 12 , 000 24 , 000 13 , 000 20 , 000 B) [ 18 , 100 13 , 000 27 , 500 9 , 000 17 , 800 15 , 900 7 , 900 14 , 800 21 , 200 ] − [ 17 , 000 13 , 000 24 , 000 8 , 000 16 , 000 13 , 000 6 , 000 12 , 000 20 , 000 ] = [ 1 , 100 2 , 700 3 , 500 1 , 000 1 , 800 2 , 900 1 , 900 2 , 800 1 , 200 ] \left[ \begin{array} { r r r } 18,100 & 13,000 & 27,500 \\9,000 & 17,800 & 15,900 \\7,900 & 14,800 & 21,200\end{array} \right] - \left[ \begin{array} { c c c c } 17,000 & 13,000 & 24,000 \\8,000 & 16,000 & 13,000 \\6,000 & 12,000 & 20,000\end{array} \right] = \left[ \begin{array} { l l l } 1,100 & 2,700 & 3,500 \\1,000 & 1,800 & 2,900 \\1,900 & 2,800 & 1,200\end{array} \right] 18 , 100 9 , 000 7 , 900 13 , 000 17 , 800 14 , 800 27 , 500 15 , 900 21 , 200 − 17 , 000 8 , 000 6 , 000 13 , 000 16 , 000 12 , 000 24 , 000 13 , 000 20 , 000 = 1 , 100 1 , 000 1 , 900 2 , 700 1 , 800 2 , 800 3 , 500 2 , 900 1 , 200 C) [ 17 , 000 13 , 000 24 , 000 8 , 000 16 , 000 13 , 000 6 , 000 12 , 000 20 , 000 ] − [ 1 , 100 2 , 700 3 , 500 1 , 000 1 , 800 2 , 900 1 , 900 2 , 800 1 , 200 ] = [ 15 , 900 10 , 300 20 , 500 7 , 000 14 , 200 10 , 100 4 , 100 9 , 200 18 , 800 ] \left[ \begin{array} { c c c } 17,000 & 13,000 & 24,000 \\8,000 & 16,000 & 13,000 \\6,000 & 12,000 & 20,000\end{array} \right] - \left[ \begin{array} { l l l } 1,100 & 2,700 & 3,500 \\1,000 & 1,800 & 2,900 \\1,900 & 2,800 & 1,200\end{array} \right] = \left[ \begin{array} { c c c } 15,900 & 10,300 & 20,500 \\7,000 & 14,200 & 10,100 \\4,100 & 9,200 & 18,800\end{array} \right] 17 , 000 8 , 000 6 , 000 13 , 000 16 , 000 12 , 000 24 , 000 13 , 000 20 , 000 − 1 , 100 1 , 000 1 , 900 2 , 700 1 , 800 2 , 800 3 , 500 2 , 900 1 , 200 = 15 , 900 7 , 000 4 , 100 10 , 300 14 , 200 9 , 200 20 , 500 10 , 100 18 , 800 D) [ 1 , 100 2 , 700 3 , 500 1 , 000 1 , 800 2 , 900 1 , 900 2 , 800 1 , 200 ] + [ 17 , 000 13 , 000 24 , 000 8 , 000 16 , 000 13 , 000 6 , 000 12 , 000 20 , 000 ] = [ 18 , 100 15 , 700 27 , 500 9 , 000 17 , 800 15 , 900 4 , 100 14 , 800 21 , 200 ] \left[ \begin{array} { l l l } 1,100 & 2,700 & 3,500 \\1,000 & 1,800 & 2,900 \\1,900 & 2,800 & 1,200\end{array} \right] + \left[ \begin{array} { c c c } 17,000 & 13,000 & 24,000 \\8,000 & 16,000 & 13,000 \\6,000 & 12,000 & 20,000\end{array} \right] = \left[ \begin{array} { c c c } 18,100 & 15,700 & 27,500 \\9,000 & 17,800 & 15,900 \\4,100 & 14,800 & 21,200\end{array} \right] 1 , 100 1 , 000 1 , 900 2 , 700 1 , 800 2 , 800 3 , 500 2 , 900 1 , 200 + 17 , 000 8 , 000 6 , 000 13 , 000 16 , 000 12 , 000 24 , 000 13 , 000 20 , 000 = 18 , 100 9 , 000 4 , 100 15 , 700 17 , 800 14 , 800 27 , 500 15 , 900 21 , 200 E) [ 17 , 000 13 , 000 24 , 000 8 , 000 16 , 000 13 , 000 6 , 000 12 , 000 20 , 000 ] − [ 15 , 900 10 , 300 20 , 500 7 , 000 14 , 200 10 , 100 4 , 100 9 , 200 18 , 800 ] = [ 1 , 100 2 , 700 3 , 500 1 , 000 1 , 800 2 , 900 1 , 900 2 , 800 1 , 200 ] \left[ \begin{array} { c c c c } 17,000 & 13,000 & 24,000 \\8,000 & 16,000 & 13,000 \\6,000 & 12,000 & 20,000\end{array} \right] - \left[ \begin{array} { c c c } 15,900 & 10,300 & 20,500 \\7,000 & 14,200 & 10,100 \\4,100 & 9,200 & 18,800\end{array} \right] = \left[ \begin{array} { l l l } 1,100 & 2,700 & 3,500 \\1,000 & 1,800 & 2,900 \\1,900 & 2,800 & 1,200\end{array} \right] 17 , 000 8 , 000 6 , 000 13 , 000 16 , 000 12 , 000 24 , 000 13 , 000 20 , 000 − 15 , 900 7 , 000 4 , 100 10 , 300 14 , 200 9 , 200 20 , 500 10 , 100 18 , 800 = 1 , 100 1 , 000 1 , 900 2 , 700 1 , 800 2 , 800 3 , 500 2 , 900 1 , 200
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