Maths. Section ALinear Programming

With respect to the following shaded feasible region (ABCDEFA), the m…

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function $z=3x+4y-2$ is at point(s):

$Shaded feasible region ABCDEFA$

Answer & explanation

Correct answer: option 4

The correct answer is Option (4) → Point E only

The maximum of z over a bounded feasible region occurs at a corner point. Reading A(2, 0), B(3, 0) and F(0, 4) from the grid, the values at the corners are:

    $A(2, 0):\ z = 6 + 0 - 2 = 4$
    $B(3, 0):\ z = 9 + 0 - 2 = 7$
    $C(4, 1):\ z = 12 + 4 - 2 = 14$
    $D(4, 3):\ z = 12 + 12 - 2 = 22$
    $E(2, 5):\ z = 6 + 20 - 2 = 24$
    $F(0, 4):\ z = 0 + 16 - 2 = 14$

So the largest value, 24, occurs only at E.