Charlie\'s Pizza orders all of its pepperoni, olives, anchovies, and mozzarella
ID: 463586 • Letter: C
Question
Charlie's Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be shipped directly from Italy. An American distributor stops by every seven weeks to take orders. Because the orders are shipped directly from Italy, they take six weeks to arrive.
Charlie's Pizza uses an average of 220 pounds of pepperoni each week, with a standard deviation of 24 pounds. Charlie's prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 98 percent probability of not stocking out on pepperoni.
Assume that the sales representative just walked in the door and there are currently 430 pounds of pepperoni in the walk-in cooler. How many pounds of pepperoni would you order? (Round your answer to the nearest whole number.)
Charlie's Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be shipped directly from Italy. An American distributor stops by every seven weeks to take orders. Because the orders are shipped directly from Italy, they take six weeks to arrive.
Charlie's Pizza uses an average of 220 pounds of pepperoni each week, with a standard deviation of 24 pounds. Charlie's prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 98 percent probability of not stocking out on pepperoni.
Explanation / Answer
Average usage of pepperoni each week = 220pounds
Standard Deviation of pepperoni usage per week = 24 pounds
98% confident limit to make out of stock = Average+2.28 *Standard Deviation
= 220+2.28*24 = 220+53.76= 273.76
In order to ensure 98% confidence and in of stock in a week , he has to have a stock of 273.76 pounds of peperoni stock.
But it as given that, the orders are taken after every 7 weeks also it is mentioned it takes minimum 6 weeks to reach. So whenever you are ordering you must place an order for (7+6) = 13 weeks of order.
So your order volume will be 13*273.76 pounds = 3558.88
But presently you have a stock of 430 pounds of pepperoni stock.
Hence the stocks to be ordered = 3558.88-430 = 3128.88 pounds to ensure 98% of confidence in stock.