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 400 pounds per day and a standard deviation of 50 pounds per day. what daily order quantity is optimal? (hint: shortage cost must be in dollars per pound.)

421.53635

Explanation:

Let,

cost of underestimating the demand = Cu  

cost of overestimating demand = Co

Cu = (Burger selling price - cost per burger) × No. of hamburgers prepared

     = ($0.60 - $0.50) × 4

     = $0.40

Co = Price of top-grade ground beef - Selling price of leftover meat

= $1 - $0.80

= $0.20

Service Level = Cu ÷ (Cu + Co)

                       =  0.40 ÷ (0.40 + 0.20)

                       = 0.40 ÷ 0.60

                       = 0.6667

Z-Value at above service level = 0.430727 (Taken from z-tables)

Optimal Order quantity = Mean + Z-Value × Standard Deviation

                                       = 400 + 0.430727 × 50

                                       = 400 + 21.53635

                                       = 421.53635