Chapter 4.4, Problem 73E

Politics. In a local California election, a public relations firm promoted its candidate in three ways: telephone calls, house calls, and letters. The cost per contact is given in matrix $M$, and the number of contacts of each type made in two adjacent cities is given in matrix $N$.

$\begin{array}{l}\text{ Cost per contact}\\ M=\left[\begin{array}{c}\$1.20\\ \$3.00\\ \text{\$1}\text{.45}\end{array}\right]\begin{array}{l}\text{Telephone call}\hfill \\ \text{House}\hfill \\ \text{Letter}\hfill \end{array}\end{array}$

$\begin{array}{l}\begin{array}{cccc}& \begin{array}{l}\text{Telephone}\\ \text{call}\end{array}& \begin{array}{l}\text{House}\\ \text{call}\end{array}& \begin{array}{l}\\ \text{Letter}\end{array}\end{array}\\ N=\left[\begin{array}{ccc}\begin{array}{l}1,000\\ 2,000\end{array}& \begin{array}{l}500\\ 800\end{array}& \begin{array}{l}5,000\\ 8,000\end{array}\end{array}\right]\begin{array}{c}\text{Berkeley}\\ \text{Oakland}\end{array}\end{array}$

(A) Find the total amount spent in Berkeley.

(B) Find the total amount spent in Oakland.

(C) If either product $MN\text{or }NM$ 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 number of telephone calls, house calls, and letters. State the matrices that can be used and perform the necessary operations.