JEE Main · MathematicsMedium

$Find the maximum value of the objective function Z = 3 x + 4 y subject to the constraints x + y \leq 4, x \geq 0, and y \geq 0 .$

A. $12$
B. $16$
C. $15$
D. $14$

Show correct answer & step-by-step solution

Correct answer: B — $16$

Solution

The feasible region is a triangle with vertices at (0, 0), (4, 0), and (0, 4) . Evaluating Z at these points gives 0, 12, and 16 respectively, so the maximum is 16 .

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