Valley Construction Company must choose between two types of cranes. Crane X costs $$600,000,$ will last for $5$ years, and will require $$50,000$ in maintenance each year. Crane Y costs $$800,000$ and will last for $7$ years and will require $$30,000$ in maintenance each year. Maintenance costs for cranes X and Y are incurred at the end of each year. The appropriate discount rate is $10\%$ per year. Which machine should the company purchase?