Burger Prince buys top$-$grade ground beef for $$\mathrm{.}80$ per pound. A large sign over the entrance guarantees that the meat is fresh daily. Any leftover meat is sold to the local high school cafeteria for $50$ cents per pound. Four hamburgers can be prepared from each pound of meat. Burgers sell for $70$ cents each. Labor, overhead, meat, buns, and condiments cost $60$ cents per burger. Demand is normally distributed with a mean of $394$ pounds per day and a standard deviation of $39$ pounds per day. What daily order quantity is optimal? $($Hint: calculate overage and shortage costs per pound.$)$

Optimal daily order quantity in pounds