A current of 11 amperes branches into currents x, y, and z through resistors with resistences 8, 2, and 3 ohms as shown. I=11 amps I=x, R=8 I=y, R=2 I=z, R=3 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.) x = y = amps amps z = amps

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