Answer
a) The amount of heat produced when the steam plant burns x1 tons of anthracite and x2 tons of bituminous coal is$27\cdot 6x_1+30\cdot 2x_2$ million Btu.
b) The total output produced by x1 tons of anthracite and x2 tons of bituminous coal is given by the vector $x_1\begin{bmatrix}27.6\\3100\\250\end{bmatrix}+x_2\begin{bmatrix}30.2\\6400\\360\end{bmatrix}$
c) The appropriate values for x1 and x2 satisfy$x_1\begin{bmatrix}27.6\\3100\\250\end{bmatrix}+x_2\begin{bmatrix}30.2\\6400\\360\end{bmatrix}=\begin{bmatrix}162\\23610\\1623\end{bmatrix}$
Work Step by Step
c)To solve, row reduce the augmented matrix:
$\begin{bmatrix}27\cdot 6\ \ \ \ \ 30\cdot 2\ \ \ \ \ \ \ \ \ 162\\3100\ \ \ \ \ 6400\ \ \ \ \ \ \ \ \ \ 23610\\250\ \ \ \ \ \ \ \ 360\ \ \ \ \ \ \ \ \ \ \ 1623\end{bmatrix}$
$\begin{bmatrix}1\cdot000\ \ \ \ \ 0\ \ \ \ \ \ \ \ \ \ 3\cdot900\\0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ \ \ \ \ \ \ \ \ 1\cdot800\\0\ \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ \ \ \ \ \ \ \ 0\end{bmatrix}$
The steam plant burned 3.9 tons of anthracite coal and 1.8 tons of bituminous coal.
