JEE Main · MathematicsHard

$Minimize Z = 3 x + 5 y subject to x + 3 y \geq 3, x + y \geq 2, x, y \geq 0 .$

A. $6$
B. $7$
C. $8$
D. $9$

Show correct answer & step-by-step solution

Correct answer: B — $7$

Solution

The corner points of the feasible region are (3, 0), (1.5, 0.5), and (0, 2) . Evaluating Z at these points gives 9, 7, and 10 respectively, so the minimum is 7 .

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