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:

$\backslash$table$[[$Setup labor cost,$$20$ per hour$],[$Annual holding cost,$$16$ per unit$],[$Daily production,$976$ units$/8$ hour day$],[$Annual demand,$23,920(260$ days each $$ daily demand of $92$ units$)],[$Desired lot size,$122$ units $($one hour of production$)]]$

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