An airline offers coach and first-class tickets for a flight to Aruba. For the airline to be profitable, it must sell a minimum of 20 first-class tickets and a minimum of 45 coach tickets. The flight must have at least 100 travelers aboard in order for the plane to take off. But the plane has a maximum capacity of 180 travelers. The airline makes a profit of $225 for each coach ticket and $200 for each first-class ticket.

Answer ALL of the following questions:

1. Create a system of constraints that model the given situation. Be sure to label all variables.

2. Graph the system of constraints and shade the feasible region.

3. Find and label all of the corner points of the feasible region.

4. Is it feasible for them to sell 150 coach tickets and 25 first class tickets? Why or why not?

Mathematically justify your decision.

5. What is the maximum number of coach tickets they can sell? What is the maximum number of first class tickets they can sell? How can you tell this from the graph?

6. How many of each ticket should be sold in order to maximize profits? What is the maximum profit they can achieve?

7. What is the minimum profit they can achieve from the flight?