For the LP problem, maximize z = 2x + 3y, the coordinates of the corner points of the bounded feasible region are $A (3, 3), B (20, 3), C (20, 10), D (18, 12)$ and $E (12, 12)$ ,the maximum value of z is

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Solution

The correct option is
C

We check the value of the $z$ at each of the corner points.
At $A (3, 3) -$
$z = 2 x + 3 y = 2 (3) + 3 (3) = 15$
At $B (20, 3) -$
$z = 2 x + 3 y = 2 (20) + 3 (3) = 49$
At $C (20, 10) -$
$z = 2 x + 3 y = 2 (20) + 3 (10) = 70$
At $D (18, 12) -$
$z = 2 x + 3 y = 2 (18) + 3 (12) = 72$
At $E (12, 12) -$
$z = 2 (12) + 3 (12) = 60$
Hence, $z$ has maximum value at $D (18, 12)$ and the maximum value is $72$

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For the LP problem, maximize z = 2x + 3y, the coordinates of the corner points of the bounded feasible region are A(3,3),B(20,3),C(20,10),D(18,12) and E(12,12) ,the maximum value of z is

For the LP problem, maximize z = 2x + 3y, the coordinates of the corner points of the bounded feasible region are $A (3, 3), B (20, 3), C (20, 10), D (18, 12)$ and $E (12, 12)$ ,the maximum value of z is