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JEE Main & Advanced Mathematics Linear Programming Question Bank Self Evaluation Test - Linear Programming

  • question_answer
    Corner points of the feasible region for an LPP are\[(0,2)\]\[(3,0)\]\[(6,0)\],\[(6,8)\] and \[(0,5)\].Let \[F=4x+6y\] be the objective function. The minimum value of F occurs at

    A) \[(0,2)\] Only

    B) \[(3,0)\] Only

    C) The mind-point of the line segment joining the points \[(0,2)\] and \[(3,\,\,2)\]only

    D) Any point on the line segment joining the points \[(0,2)\] and \[(3,0)\]

    Correct Answer: D

    Solution :

    [d] Construct the following table of objective function
    Corner point Value of \[F=4x+6y\]
    (0, 2) \[4\times 0+6\times 2=12\]
    (3, 0) \[4\times 3+6\times 0=12\]
    (6, 0) \[4\times 6+6\times 0=24\]
    (6, 8) \[4\times 6+6\times 8=72\]
    (0, 5) \[4\times 0+6\times 5=30\]
    \[\}\leftarrow \min imum\] \[\}\leftarrow \operatorname{maxi}mum\] Since the minimum value (F) =12 occurs at two distinct corner points, it occurs at every points of the segment joining these two points.


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