Beechtree Corporation sells chewing gum and during January they ran production machines for $27,000$ hours total and incurred $$10,000$ in maintenance costs. During July they ran production machines for $14,000$ hours total and incurred $$8,400$ in maintenance costs.

Based on this data, what will total maintenance costs be if the machines are run for $16,500$ hours? $($Round intermediary calculations to the nearest cent.$)$