Question:
The maximum value of the objective function $z=2x+3y$, when the corner points of the feasible region are (0, 0), (5, 0), (4, 1) and (0, 2), is:
The maximum value of the objective function $z=2x+3y$, when the corner points of the feasible region are (0, 0), (5, 0), (4, 1) and (0, 2), is:
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In Linear Programming, the optimal solution always occurs at one of the corner points.
Updated On: Apr 28, 2026
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Substitute each corner point into the objective function $z = 2x + 3y$.
Step 2: Calculation
- At (0, 0): $z = 2(0) + 3(0) = 0$ - At (5, 0): $z = 2(5) + 3(0) = 10$ - At (4, 1): $z = 2(4) + 3(1) = 8 + 3 = 11$ - At (0, 2): $z = 2(0) + 3(2) = 6$
Step 3: Conclusion
The maximum value obtained is 11 at the point (4, 1). Final Answer: (D)
Substitute each corner point into the objective function $z = 2x + 3y$.
Step 2: Calculation
- At (0, 0): $z = 2(0) + 3(0) = 0$ - At (5, 0): $z = 2(5) + 3(0) = 10$ - At (4, 1): $z = 2(4) + 3(1) = 8 + 3 = 11$ - At (0, 2): $z = 2(0) + 3(2) = 6$
Step 3: Conclusion
The maximum value obtained is 11 at the point (4, 1). Final Answer: (D)
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