HardCalculusca-042

Lagrange Multiplier Product

Problem

Maximize f(x, y) = a*x*y subject to the linear constraint b*x + c*y = d, with b and c nonzero.

The Lagrange conditions give x = d / (2*b) and y = d / (2*c). Return [x, y, f_max] where f_max = a * x * y.

Hint

Set the gradients of f and the constraint proportional and use the constraint to pin down the multiplier.

case 1

in: [1,1,1,10]

expected: [5,5,25]

case 2

in: [2,1,2,8]

expected: [4,2,16]

case 3

in: [-1,2,5,20]

expected: [5,2,-10]

case 4

in: [3,4,6,24]

expected: [3,2,18]

Starter codePython

def lagrange_product(a, b, c, d):
    # Return [x, y, f_max]
    # Your code here
    pass

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