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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 the 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 maximize profit for the airline. What is the maximum profit. Make an L.P.P. and solve it graphically.

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Best answer

Let, number of executive class tickets to be sold, be x and that of economy class be y.

∴ LPP becomes : Maximize Profit (P)

= 1000 x + 600y

Subject to : x ≥ 0, y ≥ 0

x + y ≤ 200

y ≥ 4x or 4x – y ≤ 0

x ≥ 20

For correct graph

Getting vertices of feasible region as

A(20, 180), B(40, 160), C(20, 80)

Profit at A = Rs 128000

Profit at B = Rs 136000

Profit at C = Rs 68000

∴ Max profit = Rs. 136000 for 40 executive and 160 economy tickets

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