Chapter 4.4, Problem 69E

Labor costs. A company with manufacturing plants located in Massachusetts (MA) and Virginia (VA) has labor-hour and wage requirements for the manufacture of three types of inflatable boats as given in the following two matrices:

Labor hours per boat

$\begin{array}{l}\begin{array}{ccc}\begin{array}{c}\text{Cutting}\\ \text{department}\end{array}& \begin{array}{c}\text{Assembly}\\ \text{department}\end{array}& \begin{array}{c}\text{Packaging}\\ \text{department}\end{array}\end{array}\\ M=\left[\begin{array}{ccc}\text{0}\text{.6hr }& \text{0}\text{.6hr }& \text{0}\text{.2hr}\\ \text{1}\text{.0hr }& \text{0}\text{.9hr }& \text{0}\text{.3hr}\\ \text{1}\text{.5hr }& \text{1}\text{.2hr }& \text{0}\text{.4hr}\end{array}\right]\begin{array}{l}\text{One-person that}\hfill \\ \text{Two-person boat}\hfill \\ \text{Four-person boat}\hfill \end{array}\end{array}$

Hourly wages

$\begin{array}{l}\begin{array}{ccc}& \text{MA}& \text{ VA}\end{array}\\ N=\left[\begin{array}{cc}\$17.30& \$14.65\\ \begin{array}{l}\$12.22\\ \$10.63\end{array}& \begin{array}{l}\$10.29\\ \$9.66\end{array}\end{array}\right]\begin{array}{c}\text{cuttingdepartment}\\ \text{Assembly}\text{department}\\ \text{Packaging}\text{department}\end{array}\end{array}$

(A) Find the labor costs for a one-person boat manufactured at the Massachusetts plant.

(B) Find the labor costs for a four-person boat manufactured at the Virginia plant.

(C) Discuss possible interpretations of the elements in the matrix products $MN\text{and}NM$.

(D) If either of the products $MN\text{or}NM$ has a meaningful interpretation. Find the product and label its rows and columns.