The maximum number of passengers an aeroplane can carry is 300. A profit of Rs. 1200 is made on each executive class ticket and a profit of Rs. 800 is made on each economy class ticket. The airline reserves at least 40 seats for executive class. However, at least 5 times as many passengers prefer to travel by economy class than by executive class. The maximum profit of the airline is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 2,60,000
Let x be the number of executive class tickets and y the number of economy class tickets sold.
Maximise \(Z = 1200x + 800y\)
subject to
\(x + y \le 300\) (seats)
\(x \ge 40\) (executive seats reserved)
\(y \ge 5x\) (at least 5 times as many in economy)
The feasible region is a triangle. Its corner points are where two of the boundary lines meet:
\(x = 40,\ y = 5x\): (40, 200)
\(x = 40,\ x + y = 300\): (40, 260)
\(y = 5x,\ x + y = 300\): \(6x = 300\), so (50, 250)
Value of Z at each corner:
\((40, 200): Z = 48000 + 160000 = 208000\)
\((40, 260): Z = 48000 + 208000 = 256000\)
\((50, 250): Z = 60000 + 200000 = 260000\)
The maximum profit is Rs. 2,60,000, with 50 executive and 250 economy tickets.