A current of 11 amperes branches into currents x, y, and : through resistors with resistences 6, 9, and 8 ohms as shown. [=x, R=6 [=1] amps 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 2 FR, where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find the currents x, y, and 2 which will minimize the total energy generated. (It turns out that nature always splits the currents so that the total energy is minimized.) amps amps amps N '