The corner points of the feasible region determined by the system of linear constraints are as shown in the following figure:

If $Z = 3x - 4y$ be the objective function, then find the maximum value of $Z$.

12

The correct answer is Option (2) → 12 ##

Given, $Z=3x-4y$

$Z(A) = Z(0, 8) = 3 \times 0 - 8 \times 4 = -32$

$Z(B) = Z(4, 10) = 12 - 40 = -28$

$Z(C) = Z(6, 8) = 18 - 32 = -14$

$Z(D) = Z(6, 5) = 18 - 20 = -2$

$Z(E) = Z(4, 0) = 12 - 0 = 12$

So, maximum value of $Z = 12$