P$2.($CVP for multiple products case$)$ Rowling Company produces and sells three products, product $A,$ product $B,$ and product $C.$ Over the most recent five years, Rowling sold, on average, $10,000$ units of $A,30,000$ units of $B,$ and $60,000$ units of $C,$ annually. The following information pertains to the prices and costs of the three products.

$\backslash$table$[[,A,,,],[$Price$($$$)/$unit$,20,,40,30],[$Variable costs $\frac{\text{\$}}{?}$ unit,$-14,,-22,-15],[$Contribution margin$/$unit$,6,,18,15],[$Fixed costs: $$150,000,,,,],[$Before tax Target income,$$30,000,,,]]$

Required: Assume that the sales mix is maintained.

a$.$ What is the company's break$-$even point in terms of the number of units of each product and $ $?$

b$.$ How many units of each product should be sold to earn the target income?