For the linear programming problem (LPP):

Maximize $Z = x + 1.5y$, subject to constraints, $x + 2y ≤ 40,2x + y ≤ 40,x + y ≤ 25,x ≥ 0,y ≥ 0$.

Which of the following is NOT correct?

The optimal value of the objective function is attained at the point (15, 10).

The correct answer is Option (3) → The optimal value of the objective function is attained at the point (15, 10).

Given: Maximize $Z = x + 1.5y$ subject to

$x + 2y \le 40$

$2x + y \le 40$

$x + y \le 25$

$x \ge 0,\; y \ge 0$

Find corner points (intersection of constraints / axes):

$(0,0)$

Intersect $x+2y=40$ with $x=0 \Rightarrow y=20 \Rightarrow (0,20)$

Intersect $2x+y=40$ with $y=0 \Rightarrow x=20 \Rightarrow (20,0)$

Intersect $x+2y=40$ and $x+y=25$: $y=15,\; x=10 \Rightarrow (10,15)$

Intersect $2x+y=40$ and $x+y=25$: $x=15,\; y=10 \Rightarrow (15,10)$

Evaluate $Z$ at these corner points:

$Z(0,0)=0$

$Z(20,0)=20$

$Z(15,10)=15 + 1.5(10)=15 + 15 = 30$

$Z(10,15)=10 + 1.5(15)=10 + 22.5 = 32.5$

$Z(0,20)=0 + 1.5(20)=30$

Maximum value $Z_{\max}=32.5$ occurs at the single point $(10,15)$.

Therefore the NOT correct statement is: "The optimal value of the objective function is attained at the point (15, 10)."

All other given statements are correct (feasible region is bounded; listed corner points are correct; the LPP has a unique optimal solution at $(10,15)$).