$1.$ An inventory management problem: We regularly purchase an item that has the following supply information:

$$ Cost to make a purchase $$50($S$)$

$$ Cost to hold $$25$ per year $($H$)$

$$ Cost for each item $$24$

$$ Demand is $2,500$ per year, generally spread throughout the year $($D$)$

$$ Lead time $112$ days $($T$)$

If the demand varies with a Standard Deviation of $5\%$ and we wish to be $99\%$ sure of no stock out, what should we use as a safety stock in our ordering the supply?