Question

An aeroplane can carry a maximum of 200 passengers. A profit of Rs 400 is made on each executive class ticket and a profit of Rs 300 is made on each economy class ticket. The airline reserves atleast 20 seats for executive class. However atleast 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each must be sold in order to maximize the profit for the airline. What is the maximum profit?

Answer 1

To maximize the profit for the airline, 40 executive class tickets and 160 economy class tickets should be sold. The maximum profit would be Rs 64,000.

Step-by-step explanation:

To maximize the profit for the airline, we need to determine the number of executive class and economy class tickets that should be sold. Let's assume the number of executive class tickets sold is x. According to the problem, the number of economy class tickets sold would be 4x. So, the total number of passengers would be x + 4x = 5x.

Since a maximum of 200 passengers can be carried, we can write the equation 5x ≤ 200. Solving this inequality, we find x ≤ 40.

To maximize the profit, we should sell 40 executive class tickets and 4 times that number of economy class tickets, which would be 40 x 4 = 160. The maximum profit can be calculated by multiplying the number of tickets by the profit made per ticket.

For executive class tickets, the profit is Rs 400, so the profit from selling executive class tickets would be 40 x Rs 400 = Rs 16,000. For economy class tickets, the profit is Rs 300, so the profit from selling economy class tickets would be 160 x Rs 300 = Rs 48,000. The total maximum profit for the airline would be Rs 16,000 + Rs 48,000 = Rs 64,000.