The maximum value of \( z=3x+4y \) subject to the constraints
\( x+y\ge2,\ 2x+3y\le6,\ x\ge0,\ y\ge0 \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9
The line \( x+y=2 \) meets the axes at (2, 0) and (0, 2), and the line \( 2x+3y=6 \) meets them at (3, 0) and (0, 2). The feasible region lies on or above the first line and on or below the second, so it is the triangle with corners (0, 2), (2, 0) and (3, 0).
Values of z at the corner points:
\( z(0,2)=8 \)
\( z(2,0)=6 \)
\( z(3,0)=9 \)
The maximum value is 9, at (3, 0).