Joe$$s Slop House is a little hole in the wall restaurant that serves slow$-$cooked barbecue beef sandwiches. The beef for the sandwiches cooks overnight, so each evening Joe decides how much beef to cook for the next day. The beef costs $$2\mathrm{.}5$ a pound and Joe sells each sandwich $($filled with $1$ pound of beef$)$ for $$4\mathrm{.}5.$ At the end of the day, any leftover beef is given to the neighborhood church for their soup kitchen. The tax deduction for this is worth $$2$ a pound. Daily demand for the beef can be approximated by a normal distribution with a mean of $280$ pounds and a standard deviation of $25$ pounds.

Cost of Shortage $($Cs$)$:

Cost of Excess $($Ce$)$:

What is the optimal service level?

What is the corresponding z value?

How many pounds of beef should Joe cook for the next day?