It is known that the current splits in such a way that the sum of the currents through the three

resistors equals the initial current. The energy generated in each resistor is given by E = i²R,

where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find

the currents x, y, and z which will minimize the total energy generated. (It turns out that nature

always splits the currents so that the total energy is minimized.)