GATE ME 2014 Set 3 — Question 49
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Industrial Engineering → Operations Research → LP (Graphical & Simplex)
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Question
Consider an objective function and the constraints
,
,
.
The maximum value of the objective function is _______
,
,
.
The maximum value of the objective function is _______
Correct answer
17 to 19
Solution
Step 1: Identify the feasible region defined by the constraints.
The constraint is more restrictive in the first quadrant. Its intersections with the axes are and . Both points satisfy . Thus, the vertices are , , and .Step 3: Evaluate the objective function at each vertex.
The maximum value of is 18 at the point .
1.
2.
3.
Step 2: Find the vertices of the feasible region.The constraint is more restrictive in the first quadrant. Its intersections with the axes are and . Both points satisfy . Thus, the vertices are , , and .Step 3: Evaluate the objective function at each vertex.
- At :
- At :
- At :
The maximum value of is 18 at the point .
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