Carol Cagle has a repetitive manufacturing plant producing trailer hitches in Arlington, Texas. The plant has an average inventory turnover of only $12$ times per year. He has therefore determined that

he will reduce his component lot sizes. He has developed the following data for one component, the safety chain clip:

To obtain the desired lot size, the set$-$up time that should be achieved $=3\mathrm{.}11$ minutes $($round your response to two decimal places$).$