Violet Van Patten's company Pixels makes video game systems. On average it takes $6$ hours to make each one during two $8-$hour shifts each production day, and the WIP inventory averages $233$ units. How many systems does Violet make per production day for her steady state process? Go to at least three decimal places for intermediate steps $($so $12\mathrm{.}1786$ would be rounded as $12\mathrm{.}179)$ and one decimal place for your final answer $($so $12\mathrm{.}1793$ would be rounded as $12\mathrm{.}2).$

throughput rate $($units per production day$)$