JEE Main & Advanced Mathematics Linear Programming Question Bank Critical Thinking

  • question_answer A Firm makes pents and shirts. A shirt takes 2 hour on machine and 3 hour of man labour while a pent takes 3 hour on machine and 2 hour of man labour. In a week there are 70 hour machine and 75 hour of man labour available. If the firm determine to make x shirts and y pents per week, then for this the linear constraints are 

    A)                 \[x\ge 0,\ y\ge 0,\ 2x+3y\ge 70,\ 3x+2y\ge 75\]

    B)                 \[x\ge 0,\ y\ge 0,\ 2x+3y\le 70,\ 3x+2y\ge 75\]

    C)                 \[x\ge 0,\ y\ge 0,\ 2x+3y\ge 70,\ 3x+2y\le 75\]

    D)                 \[x\ge 0,\ y\ge 0,\ 2x+3y\le 70,\ 3x+2y\le 75\]

    Correct Answer: D

    Solution :

    Type of items Working time on machine Man labour
    Shirt (x) Pent (y) 2 hours 3 hours 3 hours 2 hours
    Availability 70 hours 75 hours
                                    Linear constraints are \[2x+3y\le 70,\,3x+2y\le 75\].


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