Chapter 4.4, Problem 70E

Inventory value. A personal computer retail company sells five different computer models through three stores. The inventory of each model on hand in each store is summarized in matrix $M$. Wholesale $\left(W\right)$ and retail $\left(R\right)$ values of each model computer are summarized in matrix $N$

$\begin{array}{l}\text{ Model}\\ \begin{array}{rrrrr}\hfill A& \hfill B& \hfill C& \hfill D& \hfill E\end{array}\\ M=\left[\begin{array}{rrrrr}\hfill 4& \hfill 2& \hfill 3& \hfill 7& \hfill 1\\ \hfill 2& \hfill 3& \hfill 5& \hfill 0& \hfill 6\\ \hfill 10& \hfill 4& \hfill 3& \hfill 4& \hfill 3\end{array}\right]\begin{array}{c}\text{Store}1\\ \text{Store}2\\ \text{Store}3\end{array}\end{array}$.

$\begin{array}{l}\begin{array}{ccc}& \text{ W}& \text{ R}\end{array}\\ N=\left[\begin{array}{c}\$700\\ \$1,400\\ \begin{array}{l}\$1,800\\ \$2,700\end{array}\\ \$3,500\end{array}\begin{array}{c}\$840\\ \begin{array}{l}\$1,800\\ \$2,400\end{array}\\ \$3,300\\ \$4,900\end{array}\right]\begin{array}{c}\begin{array}{l}A\\ B\end{array}\\ C\\ \begin{array}{l}D\\ E\end{array}\end{array}\text{ Model}\end{array}$

(A) What is the retail value of the inventory at store $2$ ?

(B) What is the wholesale value of the inventory at store $3$ ?

(C) If either product $MN$ or $NM$ has a meaningful interpretation. Find the product and label its rows and columns. What do the entries represent?

(D) Discuss methods of matrix multiplication that can be used to find the total inventory of each model on hand at all three stores. State the matrices that can be used and perform the necessary operations.