A production process consists of a three$-$step operation. The scrap rate is $14$ percent for the first step and $9$ percent for the other two steps.

a$.$ If the desired daily output is $457$ units, how many units must be started to allow for loss due to scrap? $($Do not round intermediate calculations. Round up your final answer to the next whole number.$)$

b$.$ If the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? $($Do not round intermediate calculations. Round up your final answer to the next whole number.$)$

c$.$ If the scrap represents a cost of $$10$ per unit, how much is it costing the company per day for the original scrap rate $($i$.$e$.$ the Part a scrap rate$)?($Round your final answer to the nearest whole number.$)$