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  3. 12th Class
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  5. Linear Programming

12th Class Mathematics Linear Programming Question Bank Case Based (MCQs) - Linear Programming

  • question_answer
    The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let \[Z\text{ }=\text{ }px\text{ }+\text{ }qy\], where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is

    A) p = q

    B) p = 2q

    C) q = 2p

    D) q = 3p

    Correct Answer: D

    Solution :

    Value of \[Z=px+qy\] at \[\left( 15,\text{ }15 \right)=15p+15q\] and that at (0, 20) =20 q. According to given condition. We have \[15p+15q=20q\Rightarrow 15p=5q\Rightarrow q=3p.\]


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