$8.$ Charlotte Corporation sells car batteries to service stations for an average of $$30$ each. The variable cost of each battery is $$18$ and monthly fixed manufacturing costs total $$10,000.$ Other monthly fixed costs of the company total $$8,000.$

Required $(10$ points$)$:

a$.$ What is the breakeven point in batteries?

b$.$ How many batteries must Charlotte sell to achieve pretax income of $$20,000?$

c$.$ What is the breakeven point in batteries, assuming variable costs increase by $20\%$

d$.$ What is the breakeven level in batteries, assuming the selling price goes up by $10\%$ and fixed expenses increase by$$1,200?$