Question

The maximum number of passengers an aeroplane can carry is 300. A profit of ₹1200 is made on each executive class ticket and a profit of ₹800 is made on each economy class ticket. The airline reserves atleast 40 seats for executive class. However, atleast 5 times as many passengers prefer to travel by economy class than by executive class. The maximum profit of the airline is:

• A. ₹2,08,000
• B. ₹2.56,000
• C. ₹2,60,000
• D. ₹2.80,000

Answer 1

The Correct Option is C

To determine the maximum profit, we must establish the constraints and objective function for this linear programming problem. Let x represent the number of executive class tickets sold and y represent the number of economy class tickets sold.

Constraints:

• x + y ≤ 300: Total number of passengers cannot exceed 300.
• x ≥ 40: At least 40 seats are reserved for executive class.
• y ≥ 5x: At least 5 times as many passengers must prefer economy class over executive class.

Objective Function:

Maximize Profit = 1200x + 800y

We need to find the values of x and y that satisfy all constraints and maximize the profit.

Steps:

1. From y ≥ 5x, and x + y ≤ 300, substitute y in the inequality:
   x + 5x ≤ 300 → 6x ≤ 300 → x ≤ 50
2. Since x ≥ 40, x can be between 40 and 50.
3. Now check boundaries to find the maximum profit:
4. When x = 40, y = 300 - x = 300 - 40 = 260. Then calculate Profit: 1200(40) + 800(260) = ₹2,40,000.
5. When x = 50, y = 300 - 50 = 250. Then calculate Profit: 1200(50) + 800(250) = ₹2,60,000.

The maximum profit occurs when x = 50 and y = 250 with a profit of ₹2,60,000.