Cyber Chemicals uses liquid nitrogen on a regular basis. Average daily dernand is $178$ gallons with a standard deviation of $45.$ Due to a substantial ordering cost, which is estimated to be $$58$ per order $($no matter the quantity in the order$),$ Cyber currently orders from its supplier on a weekly basis. Cyber also incurs holding costs on its inventory. Cyber recognizes that its inventory is lowest at the end of the week but prefers a more realistic estimate of its average inventory. In particular, Cyber estimates its average inventory to be its average end$-$of$-$week inventory plus half of its averag