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 $N.$

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

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

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

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

(E) 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.

(F) Discuss methods of matrix multiplication that can be used to find the total inventory of all five models at each store. State the matrices that can be used and perform the necessary operations.