$3\mathrm{.}20()$ The break$-$even point is to be determined for two production methods, one manual and the other automated. The manual method requires two workers at $$16\mathrm{.}50/$hr each. Together, their production rate is $30$ units per hour. The automated method has an initial cost of $$125,000,$ a $4-$year service life, no salvage value, and annual maintenance costs $=$ $$3,000.$ No labor $($except for maintenance$)$ is required for the machine, but the power to operate it is $50$ kW $($when running$).$ Cost of electric power is $$0\mathrm{.}05$ per kWh$.$ The production rate for the automated machine is $55$ units per hour. $($a$)$ Determine the break$-$even point for the two methods, using a rate of return $=25\%.($b$)$ How many hours of operation per year would be required for each method to reach the break$-$even point?