A company currently using an inspection process in its material receiving department is trying to install an overall cost reduction program. One possible reduction is the elimination of one inspection position. This position tests material that has a defective content on the average of $0\mathrm{.}04.$ By inspecting all items, the inspector is able to remove all defects. The inspector can inspect $46$ units per hour. The hourly rate including fringe benefits for this position is $$9.$ If the inspection position is eliminated, defects will go into product assembly and will have to be replaced later at a cost of $$10$ each when they are detected in final product testing.

Assume that the line will operate at the same rate $($i$.$e$.,$ the inspection rate$)$ if the inspection operation was eliminated.

a$-1.$ If the inspector position is eliminated, what will the hourly cost of defects be$?$