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J & K CET Engineering J and K - CET Engineering Solved Paper-2015

  • question_answer
    At present, a firm manufactures 1099 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by \[\frac{dP}{dx}=100-12\sqrt{x}.\]. If the firm empower  25 more workers, then the new level of production of items is

    A)  \[2000\]   

    B)  \[2500\]  

    C)  \[3000\]   

    D)  \[3500\]

    Correct Answer: B

    Solution :

    Given, \[\frac{dP}{dx}=100-12\sqrt{x}\] \[\Rightarrow \] \[dP=(100-12\sqrt{x})dx\] On integrating both sides, we get \[P=100x-12\left( \frac{{{x}^{3/2}}}{3/2} \right)+C\] \[\Rightarrow \] \[P=100x-8{{x}^{3/2}}+C\] ?.(i) At initially \[x=0,\,\,\,\,P=1000\] Then, from Eq. (i) we get \[1000=100\times 0-0+C\] \[\Rightarrow \] \[C=1000\] On putting the value of C in Eq. (i), we get \[P=100x-8{{x}^{3/2}}+1000\] Now, at \[x=25,\] \[P=100(25)-8{{(25)}^{3/2}}+1000\] \[=2500-8(125)+100\] \[=3500-1000=2500\]


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