Georgeland Cycles makes and sells two models of electric bicycles. The Commuter $($a folding model$)$ sells for $$2,509\mathrm{.}00$ and the Tourx $($a fat$-$tire trail model$)$ sells for $$4,509\mathrm{.}00.$ Unit variable costs for the Commuter are $$1,759\mathrm{.}00$ and for the Tour$-$X $$3,209\mathrm{.}00.$ Annual fixed costs at Georgeland are $$556,150.$ The marketing manager estimates that the annual mix of sales is $30$ percent Commuter model and $70$ percent Touring model.

Required:

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

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