Additional Algo $7-6$ Inventory in a Process with Setups

A lathe is used to process an automobile part. The processing time per part is $4$ minutes. After producing $140$ units of the part, the lathe requires a $46$ minute maintenance process. Demand for the part is $11$ units per hour.

What is the maximum inventory of a part $($in units$)?$

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.