Breakeven analysis and target profit, taxes, what$-$if analysis Pome Company produces a sin$-$ gle product: the Core. The following table provides the Core$$s details:

Per unIt

Sellingprice $.............$$$30$

Materials cost $............7$

Labor cost. $..............6$

Variable overhead cost. $....2$

Sales commissions. $.......10\%$ of selling price

For the upcoming year, Pome Company expects to sell $500,000$ units of the Core, have total fixed costs of $$4,500,000,$ and face a tax rate of $30\%$ of income.

Required

$($a$)$ At the expected level of unit sales, what is the after$-$tax income? $($b$)$What is the breakeven unit sales of the Core?

$($c$)$ The marketing manager believes that if the Core$$s price is cut by $$2$ unit, sales will increase by $10\%.$ Is this change desirable from a financial perspective?

$($d$)$Ignore part $($c$)$ when answering this question. The production manager believes that if Pome Company rents a new machine, total manufacturing variable costs $($materials$,$ labor, and overhead$)$ per unit will each drop by $10\%.$ What is the annual rent for this machine so that the income with this machine will equal the income in part $($a$)?$