Chapter 2.5, Problem 62E

AIRLINE FLIGHT SCHEDULING Pacific Airlines operates three flights between Los Angeles and Hong Kong. Matrix $A$ gives the number of seats in each of three cabin classes on each flight.

$\begin{array}{l}\text{First}\text{Premium}\\ \text{class}\text{economy}\text{economy}\\ A=\begin{array}{c}\text{Flight}\text{I}\\ \text{Flight}\text{II}\\ \text{Flight}\text{III}\end{array}\left[\begin{array}{ccc}60& 80& 160\\ 50& 60& 190\\ 40& 50& 210\end{array}\right]\end{array}$

The fares per passenger (in dollars) for each class of seats are given by the matrix $B$.

$B=\begin{array}{c}\text{First}\text{class}\\ \text{Premium}\text{economy}\\ \text{economy}\end{array}\left[\begin{array}{c}6000\\ 3500\\ 1500\end{array}\right]$

The number of each type of flight operate by Pacific Airline in June is given by matrix $C$.

$\begin{array}{l}\text{Flight}\\ \text{I}\text{II}\text{III}\\ C=\left[\begin{array}{ccc}8& 6& 6\end{array}\right]\end{array}$

a. Compute $AB$ and explain what it represents.

b. Compute $CAB$ and explain its meaning.