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 $2.5 a pound and Joe sells each sandwich (filled with 1 pound of beef) for $3.0. 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 $1.0 a pound. Daily demand for the beef can be approximated by a normal distribution with a mean of 230 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?