(a) Compute AB. AB = 000 11 Explain what it represents. AB represents the total number of seats in first class. AB represents the total number of seats on flight I.. AB represents the total revenue for first class seats on all flights. AB represents the total revenue for all seats for the three flights. AB represents the total revenue for Pacific Airlines in June.
(a) Compute AB. AB = 000 11 Explain what it represents. AB represents the total number of seats in first class. AB represents the total number of seats on flight I.. AB represents the total revenue for first class seats on all flights. AB represents the total revenue for all seats for the three flights. AB represents the total revenue for Pacific Airlines in June.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.3: Matrix Approa To Solving Linear Systems
Problem 51PS
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![### Pacific Airlines Seat Allocation and Revenue Calculation
Pacific Airlines operates three flights between Los Angeles and Hong Kong. The matrix \( A \) represents the number of seats in each of the three cabin classes (First class, Premium economy, and Economy) on each flight.
#### Matrix \( A \):
\[
A = \begin{pmatrix}
50 & 70 & 140 \\
40 & 50 & 170 \\
30 & 40 & 200 \\
\end{pmatrix}
\]
- **Flight I (Row 1):** 50 First class seats, 70 Premium economy seats, 140 Economy seats.
- **Flight II (Row 2):** 40 First class seats, 50 Premium economy seats, 170 Economy seats.
- **Flight III (Row 3):** 30 First class seats, 40 Premium economy seats, 200 Economy seats.
#### Matrix \( B \):
The fares per passenger (in dollars) for each class of seats are given by matrix \( B \):
\[
B = \begin{pmatrix}
6000 \\
3500 \\
1500 \\
\end{pmatrix}
\]
- **First class:** $6000
- **Premium economy:** $3500
- **Economy:** $1500
#### Matrix \( C \):
The number of each type of flight operated by Pacific Airlines in June is given by matrix \( C \):
\[
C = \begin{pmatrix}
8 \\
6 \\
6 \\
\end{pmatrix}
\]
- **Flight I:** 8 flights
- **Flight II:** 6 flights
- **Flight III:** 6 flights
### Calculations:
#### (a) Compute \( AB \):
\[
AB = \begin{pmatrix}
& & \\
& & \\
& & \\
\end{pmatrix}
\]
**Explanation**
- \( AB \) represents the total revenue for all seats for the three flights.
#### (b) Compute \( CAB \):
\[
CAB = \begin{pmatrix}
& & \\
& & \\
& & \\
\end{pmatrix}
\]
Matrix \( CAB \) will give us the total revenue generated by Pacific Airlines in June for each type of seat class.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77247d15-844d-4e77-b205-212be8c6419e%2F454c69d8-b4d9-4e2c-9ad6-124dea27fb95%2Fcsx4axe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Pacific Airlines Seat Allocation and Revenue Calculation
Pacific Airlines operates three flights between Los Angeles and Hong Kong. The matrix \( A \) represents the number of seats in each of the three cabin classes (First class, Premium economy, and Economy) on each flight.
#### Matrix \( A \):
\[
A = \begin{pmatrix}
50 & 70 & 140 \\
40 & 50 & 170 \\
30 & 40 & 200 \\
\end{pmatrix}
\]
- **Flight I (Row 1):** 50 First class seats, 70 Premium economy seats, 140 Economy seats.
- **Flight II (Row 2):** 40 First class seats, 50 Premium economy seats, 170 Economy seats.
- **Flight III (Row 3):** 30 First class seats, 40 Premium economy seats, 200 Economy seats.
#### Matrix \( B \):
The fares per passenger (in dollars) for each class of seats are given by matrix \( B \):
\[
B = \begin{pmatrix}
6000 \\
3500 \\
1500 \\
\end{pmatrix}
\]
- **First class:** $6000
- **Premium economy:** $3500
- **Economy:** $1500
#### Matrix \( C \):
The number of each type of flight operated by Pacific Airlines in June is given by matrix \( C \):
\[
C = \begin{pmatrix}
8 \\
6 \\
6 \\
\end{pmatrix}
\]
- **Flight I:** 8 flights
- **Flight II:** 6 flights
- **Flight III:** 6 flights
### Calculations:
#### (a) Compute \( AB \):
\[
AB = \begin{pmatrix}
& & \\
& & \\
& & \\
\end{pmatrix}
\]
**Explanation**
- \( AB \) represents the total revenue for all seats for the three flights.
#### (b) Compute \( CAB \):
\[
CAB = \begin{pmatrix}
& & \\
& & \\
& & \\
\end{pmatrix}
\]
Matrix \( CAB \) will give us the total revenue generated by Pacific Airlines in June for each type of seat class.
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