Chapter 2.3, Problem 68E

Wholesale and retail Sales A company has three appliance stores that sell washers, dryers, and ranges. Matrices W and R give the wholesale and retail prices of these items, respectively. Matrices N and D give the quantities of these items sold by the three stores in November and December, respectively.

$\begin{array}{l}\begin{array}{ccc}\text{Washers}& \text{Dryers}& \text{Ranges}\end{array}\\ W=\left[300250450\right]\end{array}$

$\begin{array}{l}\begin{array}{ccc}\text{Washers}& \text{Dryers}& \text{Ranges}\end{array}\\ R=\left[500450750\right]\end{array}$

$\begin{array}{l}\begin{array}{ccc}\text{Store}\text{1}& \text{Store}\text{2}& \text{Store}\text{3}\end{array}\\ N=\left[\begin{array}{c}30\\ 20\\ 10\end{array}\begin{array}{c}40\\ 30\\ 5\end{array}\begin{array}{c}20\\ 10\\ 35\end{array}\right]\begin{array}{c}\text{Washers}\\ \text{Dryers}\\ \text{Ranges}\end{array}\end{array}$

$\begin{array}{l}\begin{array}{ccc}\text{Store}\text{1}& \text{Store}\text{2}& \text{Store}\text{3}\end{array}\\ D=\left[\begin{array}{c}20\\ 30\\ 10\end{array}\begin{array}{c}50\\ 10\\ 20\end{array}\begin{array}{c}30\\ 20\\ 30\end{array}\right]\begin{array}{c}\text{Washers}\\ \text{Dryers}\\ \text{Ranges}\end{array}\end{array}$

Determine and interpret the following matrices:

(a) $WN$

(b) $WD$

(c) $RN$

(d) $RD$

(e) $R-W$

(f) $\left(R-W\right)N$

(g) $\left(R-W\right)D$

(h) $N+D$

(i) $\left(R-W\right)\left(N+D\right)$

(j) $.95R$