Question

If the capacity of energy production is $\$15$ million and the capacity of manufacturing production is $\$20$ million, how much of each is consumed internally (in million $\$$) for capacity production?

• A. Energy $21$,
  Manufacturing $5.50$
• B. Energy $11$,
  Manufacturing $5.75$
• C. Energy $5.75$,
  Manufacturing $11$
• D. Energy $5.50$,
  Manufacturing $21$

Answer 1

Answer: (B)

Energy $11$,

Manufacturing $5.75$
Input matrix is $\left[\begin{array}{cc}.40& .25\\ .25& .10\end{array}\right]$

Capacity of production for internal energy and manufacturing is $\left[\begin{array}{c}15\\ 20\end{array}\right]$

Internal energy consumed $=$ input matrix $\times$capacityof production

$=\left[\begin{array}{cc}.40& .25\\ .25& .10\end{array}\right]\left[\begin{array}{c}15\\ 20\end{array}\right]=\left[\begin{array}{c}.40\times 15+.25\times 20\\ .25\times 15+.10\times 20\end{array}\right]=\left[\begin{array}{c}11\\ 2.75\end{array}\right]$

So, 11$millionofenergyisconsumedinternallyand$ $5.75$ in manufacturing .

Option B is correct.