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:

Setup labor cost

$$$$20$ per hour

Annual holding cost

$$$$12$ per unit

Daily production

$976$units$/8$ hour day

Annual demand

$39,600(275$ days each$\backslash$times daily demand of $144$units$)$

Desired lot size

$122$ units$($one hour of$$ production$)$

Part $2$

To obtain the desired lot$$ size, the$$ set$-$up time that should be achieved$=$

$$

enter your response here minutes $($round your response to two decimal$$ places$).$