For a LPP, the objective function is \( z=4x+3y \) and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The maximum value of \( z \) is at B (30, 20)
The shaded region is the quadrilateral OCBD, so its corner points are O(0, 0), D(40, 0), B(30, 20) and C(0, 40). Points E(0, 80) and A(60, 0) lie on the boundary lines but outside the shaded region, so they are not used. Value of z = 4x + 3y at each corner:
\( \displaystyle O(0,0):\ z=0 \)
\( \displaystyle D(40,0):\ z=160 \)
\( \displaystyle B(30,20):\ z=120+60=180 \)
\( \displaystyle C(0,40):\ z=120 \)
The maximum value is 180, at B (30, 20), and the minimum value is 0, at O, so their difference is 180.