The feasible region and optimal solution of a LPP with objective function, max.(z) = 600x + 400y, subject to :
\(x + 2y \le 12,\ 2x + y \le 12,\ x + 1.25\,y \ge 5,\ x \ge 0\) and \(y \ge 0\), is:
The feasible region and optimal solution is __________
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ABCDEA and optimal solution occurs at (4,4)
The constraints \(x + 2y \le 12\) and \(2x + y \le 12\) keep the region on the origin side of the lines DG and FB, so below the broken line D–C–B. The constraint \(x + 1.25y \ge 5\) keeps it on the far side of the line EA, away from the origin.
So the feasible region is the polygon ABCDEA, with corners A(5, 0), B(6, 0), C(4, 4), D(0, 6) and E(0, 4).
The maximum of z occurs at a corner point. Values of z = 600x + 400y:
\(z(5, 0) = 3000\)
\(z(6, 0) = 3600\)
\(z(4, 4) = 2400 + 1600 = 4000\)
\(z(0, 6) = 2400\)
\(z(0, 4) = 1600\)
The largest value is 4000, at C(4, 4). So the feasible region is ABCDEA and the optimal solution occurs at (4, 4).