The feasible region for a LPP is shown in the given figure. The maximum value of \( z=2x+5y \) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 26
The feasible region is bounded, so by the corner point method the maximum of z occurs at a corner. The corners are O(0, 0), A(7, 0), B(3, 4) and C(0, 2).
\( \displaystyle \text{At }O(0,0):\ z=0 \)
\( \displaystyle \text{At }A(7,0):\ z=2(7)+5(0)=14 \)
\( \displaystyle \text{At }B(3,4):\ z=2(3)+5(4)=26 \)
\( \displaystyle \text{At }C(0,2):\ z=2(0)+5(2)=10 \)
The largest value is 26, at B(3, 4).