Chapter 4.7, Problem 15E

Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture $\left(A\right),$ building $\left(B\right),$ and energy $\left(E\right).$ The technology matrix $M$ and final demand matrices (in billions of dollars) are

$\begin{array}{l}\begin{array}{ccc}A& B& E\end{array}\\ \begin{array}{c}A\\ B\\ E\end{array}\left[\begin{array}{ccc}0.3& 0.2& 0.2\\ 0.1& 0.1& 0.1\\ 0.2& 0.1& 0.1\end{array}\right]=M\\ D_1=\left[\begin{array}{c}5\\ 10\\ 15\end{array}\right]D_2=\left[\begin{array}{c}20\\ 15\\ 10\end{array}\right]\end{array}$

How much input from $A,B,\text{ and }E$ are required to produce a dollar’s worth of output for $B?$