Output from a process contains $0\mathrm{.}02$ proportion of defective units. Defective units that go undetected into final assemblies cost $$25$ each to replace. An inspection process, which would detect and remove all defectives, can be established to test these units. The inspector, who can test $20$ units per hour $($which matches the current production rate$),$ would be paid $$8$ per hour, including fringe benefits.

Assume that the line will operate at the same rate $($i$.$e$.,$ the current production rate$)$ regardless of whether or not the inspection operation is added.

a$-1.$ Without the inspector, what is the current hourly cost of defects?

a$-2.$ Should an inspection station be established to test all units based on costs alone?

multiple choice

Yes

No

a$-3.$ If the inspection operation is added, what would be the cost to inspect each unit? $($Round your answer to $2$ decimal places.$)$

b$.$ What would be the benefit $($or loss$)$ from establishing the inspection process? $($Input the amount as a positive value. Round your answer to $2$ decimal places.$)$