AAA Company sells products $x,Y$ and Z$.$ In $2016$ the unit selling price, variable cost per unit, and sales mix ratio of these products are as under:

$\backslash$table$[[,$Products$],[,$X$,$Y$,$Z$],[$Selling Price per unit $($$$),75,125,150],[$Variable cost per unit $($$$),40,75,90],[$Sales Mix Ratio,$2,1,3]]$

Fixed costs are $$600,000$

Required

$(1)$ Compute AAA's breakeven sales $($units$).$ Prove your answer.

$(2)$ Calculate the sales $($units$)$ required to eam a target profit $$300,000$ & Show the proof