Chapter 4.4, Problem 65E

Cost analysis. A company with two different plants manufactures guitars and banjos. Its production costs for each instrument are given in the following matrices:

$\begin{array}{l}\begin{array}{cc}\text{Plant X}& \text{ Plant Y}\end{array}\\ \begin{array}{cc}\text{ Guitar}& \text{ Banjo}\end{array}\begin{array}{cc}\text{ Guitar}& \text{ Banjo}\end{array}\\ \begin{array}{c}\text{Materials}\\ \text{Labor}\end{array}\left[\begin{array}{cc}\text{\$47}& \text{ \$39}\\ \text{\$90}& \text{ \$125}\end{array}\right]=A\left[\begin{array}{cc}\text{\$56}& \text{ \$42}\\ \text{\$84}& \text{ \$115}\end{array}\right]=B\\ \end{array}$

Find $\frac{1}{2}\left(A+B\right)$ the average cost of production for the two plants