The maximum value of $z = 3 x + 4 y$ , subject to the constraints $x + y \leq 40, x + 2 y \leq 60, x \geq 0, y \geq 0$ is :

120

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140

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100

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160

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Solution

The correct option is B $140$
Maximum value of $z = 3 x + 4 y$

Given: $x + y \leq 40, x + 2 y \leq 60, x \geq 0, y \geq 0$

We have to find maximum value of $3 x + 4 y$
in the shaded region we find value at all $4$ coordinates of shaded region
$(0, 0) \to 3 (0) + 4 (0) = 0$
$(40, 0) \to 3 (40) + 4 (0) = 120$

$(0, 30) \to 3 (0) + 4 (30) = 120$

$(20, 20) \to 3 (20) + 4 (20) = 60 + 80 = 140$

Maximum value $= 140$

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