Quarter$-$inch stainless$-$steel bolts, $11/2$ rfloor inches long are consumed in a factory at a fairly steady rate of $60$ per week. The bolts cost the plant $2$ cents each. It costs the plant $$12$ to initiate an order, and holding costs are based on an annual interest rate of $25$ percent.

$($a$)$ Determine the optimal number of bolts for the plant to purchase and the time between placement of orders.

$($b$)$ What is the yearly holding and setup cost for this item?

$($c$)$ Suppose instead of small bolts we were talking about a bulky item, such as packaging materials. What problem might there be with our analysis?