MediumCalculusca-131

Lagrange Multipliers 3-Variable

Problem

Maximize f(x, y, z) = x*y*z subject to x + y + z = s with s > 0 and x, y, z positive.

By symmetry the optimum is x = y = z = s/3, giving f_max = s^3 / 27. Return [x, y, z, f_max].

Hint

The Lagrange conditions x = y = z follow immediately from symmetry.

case 1

in: [3]

expected: [1,1,1,1]

case 2

in: [6]

expected: [2,2,2,8]

case 3

in: [9]

expected: [3,3,3,27]

case 4

in: [1]

expected: [0.3333333333333333,0.3333333333333333,0.3333333333333333,0.037037037037037035]

Starter codePython

def lagrange_product_3(s):
    # Return [x, y, z, f_max]
    # Your code here
    pass

4 test cases · run your code against them in the editor