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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible

  • calculus -

    let the second number be x,
    let the first number be y
    so y + 4x = 1000, ---> y = 1000-x

    Product = xy
    = x(1000-4x)
    = 1000x - 4x^2

    find d(product)/dx
    set it equal to zero and solve for x
    comes out very nice.

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