Production of 1 unit of cologne requires 0.9 units of perfume and 0.4 units of cologne. Into 1 unit of perfume goes 0.2 unit of perfume and 0.5 units of cologne. With sector 1 as cologne and sector 2 as perfume, set up the technology matrix A.
A) $A = \left[ \begin{array} { l l }
0.2 & 0.4 \
0.9 & 0.5
\end{array} \right]$
B) $A = \left[ \begin{array} { l l }
0.2 & 0.4 \
0.5 & 0.9
\end{array} \right]$
C) $A = \left[ \begin{array} { c c }
0.4 & 0.5 \
0.9 & 0
\end{array} \right]$
D) $A = \left[ \begin{array} { l l }
0.4 & 0.5 \
0.9 & 0.2
\end{array} \right]$
E) $A = \left[ \begin{array} { l l }
0.5 & 0.4 \
0.9 & 0.2
\end{array} \right]$

Question

Production of 1 unit of cologne requires 0.9 units of perfume and 0.4 units of cologne. Into 1 unit of perfume goes 0.2 unit of perfume and 0.5 units of cologne. With sector 1 as cologne and sector 2 as perfume, set up the technology matrix A.  
A)  $A = \left[ \begin{array} { l l } 
0.2 & 0.4 \
0.9 & 0.5
\end{array} \right]$
B)   $A = \left[ \begin{array} { l l } 
0.2 & 0.4 \
0.5 & 0.9
\end{array} \right]$
C)   $A = \left[ \begin{array} { c c } 
0.4 & 0.5 \
0.9 & 0
\end{array} \right]$
D)    $A = \left[ \begin{array} { l l } 
0.4 & 0.5 \
0.9 & 0.2
\end{array} \right]$
E)   $A = \left[ \begin{array} { l l } 
0.5 & 0.4 \
0.9 & 0.2
\end{array} \right]$

Quizplus · Accepted Answer

The technology matrix A is constructed based on the inputs required for each sector. For sector 1 (cologne), 0.4 units of cologne and 0.9 units of perfume are required. For sector 2 (perfume), 0.5 units of cologne and 0.2 units of perfume are required. Thus, the matrix is arranged with cologne as the first row and perfume as the second row, reflecting the inputs into each sector correctly.

Production of 1 Unit of Cologne Requires 0 A=[0.20.40.90.5]A = \left[ \begin{array} { l l } 0.2 & 0.4 \\0.9 & 0.5\end{array} \right]A=[0.20.9​0.40.5​]

Production of 1 Unit of Cologne Requires 0 $A = \left[ \begin{array} { l l } 0.2 & 0.4 \\0.9 & 0.5\end{array} \right]$