csat-suneung 2005 Q8

csat-suneung · South-Korea · csat__math-humanities 3 marks Matrices Matrix Algebra and Product Properties
The following table shows the manufacturing cost per unit, selling price, and sales volume for two products A and B produced by a company last year.
CategoryProduct AProduct B
Manufacturing Cost$a _ { 11 }$$a _ { 12 }$
Selling Price$a _ { 21 }$$a _ { 22 }$

Sales VolumeFirst HalfSecond Half
A$b _ { 11 }$$b _ { 12 }$
B$b _ { 21 }$$b _ { 22 }$

Represent the above tables as matrices $A = \left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\ a _ { 21 } & a _ { 22 } \end{array} \right)$ and $B = \left( \begin{array} { l l } b _ { 11 } & b _ { 12 } \\ b _ { 21 } & b _ { 22 } \end{array} \right)$ respectively, and let the product of these two matrices be $A B = \left( \begin{array} { l l } a & b \\ c & d \end{array} \right)$. When the profit per unit is defined as the selling price minus the manufacturing cost, select all correct statements from . [3 points]
ㄱ. $a + b$ is the total manufacturing cost of products sold in the first half of last year. ㄴ. $c + d$ is the total selling amount of products sold throughout last year. ㄷ. $d - b$ is the total profit from products sold in the second half of last year.
(1) ㄱ
(2) ㄴ
(3) ㄱ, ㄷ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
The following table shows the manufacturing cost per unit, selling price, and sales volume for two products A and B produced by a company last year.

\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
Category & Product A & Product B \\
\hline
Manufacturing Cost & $a _ { 11 }$ & $a _ { 12 }$ \\
\hline
Selling Price & $a _ { 21 }$ & $a _ { 22 }$ \\
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{ | r | c | c | }
\hline
Sales Volume & First Half & Second Half \\
\hline
A & $b _ { 11 }$ & $b _ { 12 }$ \\
\hline
B & $b _ { 21 }$ & $b _ { 22 }$ \\
\hline
\end{tabular}
\end{center}

Represent the above tables as matrices $A = \left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\ a _ { 21 } & a _ { 22 } \end{array} \right)$ and $B = \left( \begin{array} { l l } b _ { 11 } & b _ { 12 } \\ b _ { 21 } & b _ { 22 } \end{array} \right)$ respectively, and let the product of these two matrices be $A B = \left( \begin{array} { l l } a & b \\ c & d \end{array} \right)$. When the profit per unit is defined as the selling price minus the manufacturing cost, select all correct statements from <Remarks>. [3 points]

<Remarks>\\
ㄱ. $a + b$ is the total manufacturing cost of products sold in the first half of last year.\\
ㄴ. $c + d$ is the total selling amount of products sold throughout last year.\\
ㄷ. $d - b$ is the total profit from products sold in the second half of last year.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ