Question

Burger Prince buys top-grade ground beef for $1.00 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 80 cents per pound. Four hamburgers can be prepared from each pound of meat. Burgers sell for 60 cents each. Labor, overhead, meat, buns, and condiments cost 50 cents per burger. Demand is normally distributed with a mean of 301 pounds per day and a standard deviation of 37 pounds per day. What daily order quantity is optimal? (Hint: Shortage cost must be in dollars per pound.)

Answer 1

The optimal order quantity is 316 pounds

Step-by-step explanation:

In order to calculate What daily order quantity is optimal, we have to calculate first The cost of underestimating the demand Cu and cost of overestimating demand Co

Cu = ($0.60 - $0.50)*4 = $0.40

Co = $1 - $0.80 = $0.20

Next we have to calculate the Service Level = Cu / (Cu + Co)

= 0.40 / (0.40 + 0.20)

= 0.40/0.60

= 0.6667

So, Z Value at above service level = 0.430727

Therefore, in order to calculate the Optimal Order quantity, we would have to use the following formula

Optimal Order quantity= Mean + Z Value × Std Deviation

= 301 + 37 * 0.430727

= 301 + 15.36899

= 316 pounds