An arc welding $$DC$$ power source has a linear power source characteristic with open circuit voltage $${V_O} = \,\,80$$ volts and short circuit current $${{\rm I}_S} = 1000amps.$$ The voltage-length characteristic of the arc is given by $$V=20+4L$$ volts where $$L$$ is the arc length in $$mm,$$ calculate the optimum length of arc for obtaining maximum arc power at welding. What voltage and current setting should be done on the power source for maximum arc power.