Chapter 2.5, Problem 62E

PRODUCTION PLANNING The total output of the loudspeaker systems of Acrosonic Company at their three production facilities for May and June is given by matrices $A$ and $B$ respectively. Where

$\begin{array}{l}\text{Model}\\ \text{A}\text{B}\text{C}\text{D}\\ A=\begin{array}{c}\text{Location}\text{I}\\ \text{Location}\text{II}\\ \text{Location}\text{III}\end{array}\left[\begin{array}{cccc}320& 280& 460& 280\\ 480& 360& 580& 0\\ 540& 420& 200& 880\end{array}\right]\end{array}$

$\begin{array}{l}\text{Model}\\ \text{A}\text{B}\text{C}\text{D}\\ B=\begin{array}{c}\text{Location}\text{I}\\ \text{Location}\text{II}\\ \text{Location}\text{III}\end{array}\left[\begin{array}{cccc}210& 180& 330& 180\\ 400& 300& 450& 40\\ 420& 280& 180& 740\end{array}\right]\end{array}$

The unit production cost and selling prices for these loudspeakers are given by matrices $C$ and $D$ respectively, where,

$C=\begin{array}{c}\text{Model}\text{A}\\ \text{Model}\text{B}\\ \text{Model}\text{C}\\ \text{Model}\text{D}\end{array}\left[\begin{array}{c}120\\ 180\\ 260\\ 500\end{array}\right]$

And

$D=\begin{array}{c}\text{Model}\text{A}\\ \text{Model}\text{B}\\ \text{Model}\text{C}\\ \text{Model}\text{D}\end{array}\left[\begin{array}{c}160\\ 250\\ 350\\ 700\end{array}\right]$

Compute the following matrices and explain the meaning of entries in each matrix.

a. $AC$ b. $AD$ c. $BC$ d. $BD$ e. $\left(A+B\right)C$

f. $\left(A+B\right)D$ g. $A\left(D-C\right)$ h. $B\left(D-C\right)$

i. $\left(A+B\right)\left(D-C\right)$