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
$\begin{bmatrix} 0.50 \\ 0.20 \\ 0.15 \end{bmatrix}$ a = and b = $\begin{bmatrix} 0.45 \\ 0.20 \\ 0.15 \end{bmatrix}$
Then a and b represent the \"costs per dollar of income\" for the two products. Suppose the company manufactures $x_1$ dollars
worth of product A and $x_2$ dollars worth of product B and that its total costs for materials are $140, its total costs for labor are $6
and its total costs for overhead are $45. Determine $x_1$ and $x_2$, the dollars worth of each product produced. Include a vector
equation as part of your solution.
