GATE ME 2023 Set 1 — Question 14
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Industrial Engineering → Operations Research → LP (Graphical & Simplex)
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Question
Which one of the options given represents the feasible region of the linear programming model:
Correct answer
(B) Region Q
Solution
To find the feasible region, we plot the boundary lines for each constraint and determine the half-plane satisfied by the inequality:
1.Constraint 1: . This is the region to the left of the vertical line .
2.Constraint 2: . This is the region below the horizontal line .
3.Constraint 3: . The line has intercepts at and . The inequality represents the region above and to the right of this line.
4.Constraint 4: . The line has intercepts at and . The inequality represents the region below and to the left of this line.
Intersection Analysis:- The intersection of , , and forms a triangular region.
- Vertices of this triangle:
- Intersection of and :
- Intersection of and :
- Intersection of and :
- All these points satisfy , making that constraint redundant for this specific intersection.
- Comparing this with the provided graph, the region bounded by these vertices is labeled as Region Q.
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