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JEE Main & Advanced AIEEE Solved Paper-2013

  • question_answer
    At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by\[\frac{dp}{dx}=100-12\sqrt{x}\]. If the firm employs 25 more workers, then the new level of production of items is:     AIEEE Solevd Paper-2013

    A) 2500

    B)                        3000      

    C)        3500      

    D)        4500

    Correct Answer: C

    Solution :

    \[\frac{dp}{dx}=100-12\sqrt{x}\] \[P=100x-12.\frac{2}{3}{{x}^{3/2}}+C\] \[P=100x-8{{x}^{3/2}}+C\]                           ? (1) Given if \[x=0,\text{ }P=2000\] \[\Rightarrow \]\[C=2000\] So, (1) becomes \[P=100\text{ }x-8{{x}^{3/2}}+2000\] If\[x=25\](is 25 move workers) \[P=100\times 25-8\times {{({{5}^{2}})}^{3/2}}+2000\] \[=2500-1000+2000=3500\]


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