For linear programming problem maximize \( z=2x+3y \)
Subject to the constraints \( x+y\le 4 \)
\( x\le 2 \)
\( x\ge 0,y\ge 0 \)
Maximum value of z is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12
The feasible region is bounded by x = 0, y = 0, x = 2 and x + y = 4. Its corner points come from the boundary lines (x = 2 meets x + y = 4 at (2, 2)).
By the corner point method, z = 2x + 3y at each corner is:
\( \displaystyle (0,0):\ z=0 \)
\( \displaystyle (2,0):\ z=4 \)
\( \displaystyle (2,2):\ z=4+6=10 \)
\( \displaystyle (0,4):\ z=12 \)
The region is bounded, so the maximum is the largest of these: z = 12 at (0, 4).