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5. An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?
Answers (1)
Let the airline sell x tickets of executive class and y tickets of economy class.
The mathematical formulation of the given problem is as follows:
Minimize :
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
| corner points |
|
|
| |
68000 | |
|
|
136000 | maximum |
| |
128000 | |
therefore 136000 is the maximum value of Z.
Hence, Z has a maximum value of 136000 at point
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