Question $5$

Problem $566404$:

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 $$4$ a pound and Joe sells each sandwich $($filled with $1$

pound of beef$)$ for $$5\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 $$1$ 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 $35$

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?