Do not include anything other than numbers in your responses. For example, do not include

comma or dollar sign in your numbers. As a rule of thumb, keep $2$ decimal places for larger

numbers and $3$ decimal places for smaller numbers less than $1.$

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$ 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 $$0\mathrm{.}5$ a pound. Daily demand for

the beef can be approximated by a normal distribution with a mean of $270$ pounds and a standard

deviation of $40$ 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?