The maximum value of \( Z=3x+2y \) subject to the constraints \( x+2y\ge 8, \) \( x+y\le 10,x\ge 0,y\ge 0 \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30
The feasible region lies between the lines x + 2y = 8 and x + y = 10 in the first quadrant, and is bounded.
x + 2y = 8 meets the axes at (8, 0) and (0, 4).
x + y = 10 meets the axes at (10, 0) and (0, 10).
The corner points and the values of Z are:
At (8, 0): Z = 24
At (10, 0): Z = 30
At (0, 10): Z = 20
At (0, 4): Z = 8
The maximum value of Z is 30.