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  • Oct 3, 2012, 08:58 AM
    merryd
    Optimization
    Find 2 positive numbers that satisfy the requirements that the sum of the first and twice the second is 100 and the product is a maximum.
  • Oct 3, 2012, 11:35 AM
    Abhimanyu Pudi
    50 and 25...

    Suppose the numbers to be x and y.

    x+2y=100
    then, y=1/2(100-x)

    Let xy=z
    Convert the left equivalent into x-terms and we get,
    x/2(100-x) = z
    To get the value of x when z is maximum, you need to differentiate the above equation and equal it to zero. That is,

    1/2(100-2x) = 0 and we get x=50 and so, y=25

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