Question

An aeroplane is carrying 1275 passenger. they have paid Rs 480675 as the fare. how much money did each passenger pay?​

Answer 1

Step-by-step explanation:

Let's assume that executive class ticket sold be X and economy class ticket sold be Y.

Since, aeroplane can carry maximum 200 passengers.

∴X+Y≤200 ...(1)

Since, atleast 20 tickets is reserves for executive class.

∴X≥20 ...(2)

Since the number of tickets for economy class should be at least 4 times the executive class.

∴Y≥4X⇒Y−4X≥0 ...(3)

Also, the number of tickets can't be negative.

So, X≥0 and Y≥0 ...(4)

Profit on an executive class ticket is 1000 Rs and profit on an economy class ticket is 600 Rs

So, Total profit (Z)=1000X+600Y

We have to maximize the total profit. After plotting all the constraints given by equation (1), (2), (3) and (4), we get the feasible region as shown in the image.

Corner points Value of Z=1000X+600Y

A (20, 180) 128000

B (40, 160) 136000 (Maximum)

C (20,80) 68000

Hence, maximum profit will be 136000 Rs, when number of executive class ticket sold be 40 and number of economy class ticket sold be 160