Chapter 4, Problem 45RE

Labor costs. A company with manufacturing plants in California and Texas has labor-hour and wage requirements for the manufacture of two inexpensive calculators as given in matrices $M$ and $N$ below:

$\begin{array}{l}\text{Labour}\text{hours}\text{per}\text{calculator}\\ \begin{array}{ccc}\begin{array}{l}\text{Fabricating}\\ \text{department}\end{array}& \begin{array}{l}\text{Assembly}\\ \text{department}\end{array}& \begin{array}{l}\text{Packaging}\\ \text{department}\end{array}\end{array}\\ M=\left[\begin{array}{ccc}0.15\text{hr}& 0.10\text{hr}& \text{0}\text{.05 hr}\\ 0.25\text{hr}& 0.20\text{hr}& 0.05\text{hr}\end{array}\right]\begin{array}{c}\text{Model}A\\ \text{Model}B\end{array}\end{array}$

$\begin{array}{l}\text{ Hourly}\text{Wages}\\ \begin{array}{cc}\begin{array}{l}\text{California}\\ \text{plant}\end{array}& \begin{array}{l}\text{Texas}\\ \text{plant}\end{array}\end{array}\\ N=\left[\begin{array}{cc}\$12& \$10\\ \$15& \$12\\ \$7& \$6\end{array}\right]\begin{array}{c}\text{Fabricating department}\\ \text{Assembly department}\\ \text{Packaging department}\end{array}\end{array}$

(A) Find the labor cost for producing one model $B$ calculator at the California plant.

(B) Discuss possible interpretations of the elements in the matrix products $MN$ and $NM$.

(C) If either product $MN$ or $NM$ has a meaningful interpretation, find the product and label its rows and columns.