A vacuum cleaner retailer has been selling $84$ units per month of the basic Bissell stick model for $$80.$ The retailer$$s variable costs for that model are $$51.$

$($a$)$ If a retail manager has only the information provided above, calculate the breakeven sales level for lowering the price of the basic Bissell stick model to $$72.$ Show your work.

$($b$)$ Assume that the retail manager then finds out that when a customer buys a Bissell stick model, the customer also spends an average of $$20$ for vacuum cleaner bags and that the retailer$$s contribution margin on vacuum cleaner bags is $55\%.$ Given this additional information, recalculate the breakeven sales level for lowering the price of the basic Bissell stick model to $$72.$ Again, show your work.

$($c$)$ Would having the additional information about the vacuum cleaner bags make it easier for the manager to make more profit from the price decrease or would it make it harder for her to do so$?$ Explain your reasoning.