Georgeland Cycles makes and sells two models of electric bicycles. The Commuter $($a folding model$)$ sells for $$2,514\mathrm{.}00$ and the Tour$-$X $($a fat$-$tire trail model$)$ sells for $$4,514\mathrm{.}00.$ Unit variable costs for the Commuter are $$1,764\mathrm{.}00$ and for the Tour$-$X $$3,214\mathrm{.}00.$ Annual fixed costs at Georgeland are $$612,900.$ The marketing manager estimates that the annual mix of sales is $30$ percent Commuter model and $70$ percent Touring model.

Required:

How many of each model ebike must Georgeland Cycles sell every year to break even?

How many of each model ebike must Georgeland Cycles sell every year to earn operating profits of $$102,150$ before taxes?