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

  • question_answer
    Shamli wants to invest 50,000 in saving certificates and PPF. She wants to invest at least 15,000 in saving certificate and at least 20, 000 in PPF. The rate of interest on saving certificates is \[8%P.a.\]and that on PPF is 9% P. a formulation of the above problem as LPP to determine maximum Yearly income, is

    A) Maximize \[Z=0.08x+0.09y\] subject to, \[x+y\le 50,000,x\ge 15000,\]

    B) Maximize \[Z=0.08x+0.09y\] subject o, \[x+y\le 50,000,x\ge 15000,y\le 20,000\]

    C) Maximize \[Z=0.08x+0.09y\]subject to, \[x+y\le 50,000,x\le 15000,y\ge 20,000\]

    D) Maximize \[Z=0.08x+0.09y\] subject to, \[x+y\le 50,000,x\le 15000,y\le 20,000\]

    Correct Answer: A

    Solution :

    [a] Let shamili invest x in saving certificate and y in PPF. \[\therefore x+y\le 50000,x\ge 15000andy\ge 20000\] Total income \[=\frac{8}{100}x+\frac{9}{100}y\] \[\therefore \] Given problem can be formulated as Maximize \[Z=0.08x+0.09y\] Subject to, \[x+y\le 50000,x\ge 15000,y\ge 20000.\]


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