The feasible region for an LPP is shown in figure. The maximum value of the objective function \(Z=3x+4y\) is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 100
The shaded region is bounded, with corner points O(0, 0), C(25, 0), B(20, 10) and E(0, 20). The maximum of Z is at one of them:
\(Z(0, 0)=0\)
\(Z(25, 0)=75\)
\(Z(20, 10)=60+40=100\)
\(Z(0, 20)=80\)
The maximum value is 100, at B(20, 10).
The points D(0, 50) and (40, 0) are on the boundary lines but outside the shaded region, so they are not used (Z(0, 50) = 200 and Z(40, 0) = 120 are not attainable).