The feasible region for an LPP is shown as a shaded portion in the figure given below :
Then the value of the objective function Z = 2x + 3y at B is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 48
B is the intersection of the two boundary lines. The line through D(0, 40) and A(20, 0) is
\( \displaystyle 2x+y=40 \)
The line through C(0, 10) and (30, 0) is
\( \displaystyle x+3y=30 \)
From the second line, \( x=30-3y \). Substituting in the first,
\( \displaystyle 2(30-3y)+y=40 \)
\( \displaystyle 60-5y=40\ \Rightarrow\ y=4 \)
\( \displaystyle x=30-12=18 \)
So B is (18, 4), and
\( \displaystyle Z=2(18)+3(4) \)
\( \displaystyle =48 \)