A machine costing $$257,500$ with a four$-$year life and an estimated salvage value of $$20,00$ is service on January $1.$ It is estimated that the machine will produce $475,000$ units total, and will produce $220,000$ units its first year of service. Calculate the depreciate expense for the first year of service using the $($a$)$ straight$-$line method; $($b$)$ production method; $($c$)$ double declining balance method.