‹ Back to the paper
Solve the following linear programming problem.
A linear programming problem (LPP) is given as: Maximize subject to the constraints Based on the…
A linear programming problem (LPP) is given as:
Maximize $Z = x + 2y$ subject to the constraints
$x - y \ge 0, 2 \ge 2y - x, x \ge 0, y \ge 0$
Based on the above information, answer the following questions.
(a)[1.3333333333333333]
Find the corner points of the feasible region.
(b)[1.3333333333333333]
Find the corner point where maximum occurs.
(c)[1.3333333333333333]
Optimum solution does not exist. Justify your answer.
Answer
Answer (a)
Official answer key$(0,0), (2,2)$.
Final answer: $(0,0), (2,2)$
Answer (b)
Official answer key$(2,2)$
Final answer: $(2,2)$
Answer (c)
Official answer keyAt $(2,2)$, $z = x + 2y = 6$. As the feasible region is unbounded, hence, largest value $6$ may or may not be maximum.
After plotting half plane $x + 2y > 6$, we found that there are common points with feasible region. Hence, optimum solution does not exist.
From ISC 2025 Practice Mathematics, question 94.
Check your working with the LPP solver (graphical method): linear programming by the graphical method: the feasible region drawn, corner points and the optimum.