JL$\mathrm{.}53$ Bob's Bumpers has a repetitive manufacturing facility in Kentucky that makes automobile bumpers and other auto body parts. The facility operates $270$ days per year and has annual demand of $68,000$ bumpers. They can produce up to $375$ bumpers each day. It costs $$55$ to set up the production line to produce bumpers. The cost of each bumper is $$132$ and annual holding costs are $$30$ per unit. Setup labor cost is $$20$ per hour.

What is the optimal size of the production run for bumpers? $($Display your answer to the nearest whole number.$)$

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Based on your answer to the previous question, and assuming the manufacturer holds no safety stock, what would be the average inventory for these bumpers? $($Display your answer to the nearest whole number.$)$

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