Chapter 2, Problem 20RE

Equipment Sales A company makes backyard playground equipment such as swing sets, slides, and play sets. The cost (in dollars) to make a specific style of each piece is given in matrix C. The sales price (in dollars) for each piece is given in matrix S. Two stores sell these specific pieces, and matrix A gives the quantities sold during one month.

$C=\left[\begin{array}{c}165\\ 65\\ 210\end{array}\right]\begin{array}{c}\text{Swing}\text{Set}\\ \text{Slide}\\ \text{Play}\text{Set}\end{array}$

$S=\left[\begin{array}{c}200\\ 80\\ 250\end{array}\right]\begin{array}{c}\text{Swing}\text{Set}\\ \text{Slide}\\ \text{Play}\text{Set}\end{array}$

$\begin{array}{l}\text{Swing}\text{Set}\text{Slide}\text{Play Set}\\ A=\left[\begin{array}{c}15\\ 10\end{array}\begin{array}{c}20\\ 17\end{array}\begin{array}{c}8\\ 12\end{array}\right]\end{array}$

Determine and interpret the following matrices:

(a) $AC$

(b) $AS$

(c) $S-C$

(d) $A\left(S-C\right)$