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  4. The maximum value of z = 3x + 4y subject to the condition x + y le 40, x + 2y le 60, x,y ge 0 is

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Q. The maximum value of $z = 3x + 4y$ subject to the condition $x + y \le 40, x + 2y \le 60, x,y \ge 0$ is

Linear Programming

Solution:

Obviously, $z = 3x + 4y$ will be maximum at $(20,\, 20)$
$\therefore $ Max $z = 3 × 20 + 4 × 20 = 60 + 80 = 140$