$1.$ The injection molding department of a company that operates $24$x$7$ uses an average of $30$ gallons of special lubricant per day. The usage of lubricant is normally distributed with a standard deviation of $4\mathrm{.}6$ gallons per day and it takes $3$ weeks for an order of lubricant to be delivered. If safety stock is set equal to $3$ days of average demand, what is the reorder point?

Daily Demand $($D$)=30$ gallons

Lead Time $($LT$)=3$ weeks $=(3)(7$ days$)=21$ days

Standard Deviation $=4\mathrm{.}6$ gallons

Safety stock $=3$ days $*$ Average Demand $=3(30$ gallons$)=90$ gallons

Standard Deviation $=4\mathrm{.}6$ gallons

Formula Needed:

$($D$*$LT$)+$ Safety Stock

$=($D$*$LT$)+$ Safety Stock

$=(30*21)+90$

$=720$ gallons