Solve the Problem

Solve the problem.
-A company manufactures two products. For $1.00 worth of product A, the company
spends $0.50 on materials, $0.20 on labor, and $0.15 on overhead. For $1.00 worth of
product B, the company spends $0.45 on materials, $0.20 on labor, and $0.15 on overhead.
Let $$\mathbf { a } = \left[ \begin{array} { l } 0.50 \\0.20 \\0.15\end{array} \right] \text { and } \mathbf { b } = \left[ \begin{array} { l } 0.45 \\0.20 \\0.15\end{array} \right]$$ $$\begin{array} { l } x _ { 1 } a + x _ { 2 } \mathbf { b } = \left[ \begin{array} { r } 140 \\60 \\45\end{array} \right] \\\text { or } \\x _ { 1 } \left[ \begin{array} { l } 0.50 \\0.20 \\0.15\end{array} \right] + x _ { 2 } \left[ \begin{array} { l } 0.45 \\0.20 \\0.15\end{array} \right] = \left[ \begin{array} { r } 140 \\60 \\45\end{array} \right] \\x _ { 1 } = 100 , x _ { 2 } = 200\end{array}$$