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(A) Let the airline sell $x$ tickets of executive class and $y$ tickets of economy class.The mathematical formulation of the given problem is as follo

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$136000$

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(A) Let the airline sell $x$ tickets of executive class and $y$ tickets of economy class.The mathematical formulation of the given problem is as follows:Maximize $z = 1000x + 600y$ ...... $(1)$Subject to the constraints:$x + y \leq 200$ ...... $(2)$$x \geq 20$ ...... $(3)$$y \geq 4x$ ...... $(4)$$x, y \geq 0$ ...... $(5)$The feasible region is determined by the intersection of these constraints. The corner points of the feasible region are $A(20, 80)$,$B(40, 160)$,and $C(20, 180)$.The values of $z$ at these corner points are as follows:Corner point$z = 1000x + 600y$$A(20, 80)$$1000(20) + 600(80) = 20000 + 48000 = 68000$$B(40, 160)$$1000(40) + 600(160) = 40000 + 96000 = 136000$ (Maximum)$C(20, 180)$$1000(20) + 600(180) = 20000 + 108000 = 128000$The maximum value of $z$ is $136000$ at point $B(40, 160)$.Thus,$40$ tickets of executive class and $160$ tickets of economy class should be sold to maximize the profit,and the maximum profit is $Rs. 136000$.

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