Corner points of the bounded feasible region for an LP problem are $A (0, 5) B (0, 3) C (1, 0) D (6, 0)$ . Let $z = - 50 x + 20 y$ be the objective function. Minimum value of z occurs at ______ center point.

(0, 5)

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(1, 0)

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(6, 0)

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(0, 3)

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Solution

The correct option is B $(6, 0)$
We check the value of the $z$ at each of the corner points.
At $A (0, 5) -$
$z = - 50 x + 20 y = - 50 (0) + 20 (5) = 100$
At $B (0, 3) -$
$z = - 50 x + 20 y = - 50 (0) + 20 (3) = 60$
At $C (1, 0) -$
$z = - 50 x + 20 y = - 50 (1) + 20 (0) = - 50$
At $D (6, 0) -$
$z = - 50 x + 20 y = - 50 (6) + 20 (0) = - 300$
Hence, we see that $z$ is minimum at $D (6, 0)$ and minimum value is $- 300$ .

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Corner points of the bounded feasible region for an LP problem are A(0,5)B(0,3)C(1,0)D(6,0). Let z=−50x+20y be the objective function. Minimum value of z occurs at ______ center point.

Corner points of the bounded feasible region for an LP problem are $A (0, 5) B (0, 3) C (1, 0) D (6, 0)$ . Let $z = - 50 x + 20 y$ be the objective function. Minimum value of z occurs at ______ center point.