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The Following Tables Give Annual Production Costs and Profits at Gauss

Question 133

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The following tables give annual production costs and profits at Gauss Jordan Sneakers.
 Production costs 200120022003 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 200120022003 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}
Write the matrix algebraic formula to compute the revenues from each sector each year.


A) [1,1002,7003,5001,0001,8002,9001,9002,8001,200]+[15,90010,30020,5007,00014,20010,1004,1009,20018,800]=[17,00013,00024,0008,00016,00013,0006,00012,00020,000]\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]

B) [18,10013,00027,5009,00017,80015,9007,90014,80021,200][17,00013,00024,0008,00016,00013,0006,00012,00020,000]=[1,1002,7003,5001,0001,8002,9001,9002,8001,200]\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]

C) [17,00013,00024,0008,00016,00013,0006,00012,00020,000][1,1002,7003,5001,0001,8002,9001,9002,8001,200]=[15,90010,30020,5007,00014,20010,1004,1009,20018,800]\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]

D) [1,1002,7003,5001,0001,8002,9001,9002,8001,200]+[17,00013,00024,0008,00016,00013,0006,00012,00020,000]=[18,10015,70027,5009,00017,80015,9004,10014,80021,200]\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]

E) [17,00013,00024,0008,00016,00013,0006,00012,00020,000][15,90010,30020,5007,00014,20010,1004,1009,20018,800]=[1,1002,7003,5001,0001,8002,9001,9002,8001,200]\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]

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