$5-$ A company sells two products, X and Y on a $3$:$1$ ratio. The sales price for X is $$50$ with a variable cost of $40\%$ of the sales price. The sales price for Y is $$80$ with a variable cost of $55\%$ of the sales price. Fixed costs for the firm are $$510,000.$

Question: Determine the break$-$even point

Alternatives:

A$.$ X: $425,000$; Y: $$1,062,500$

B$.$ X: $$634,286$; Y: $$145,714$

C$.$ X: $$607,143$; Y: $$323,809$

D$.$ X: $$637,000$; Y: $$283,360$

E$.$ None of the above