Instructions:

The following scenario represents two decision making challenges for a small business. You are required to analyze the information provided and make recommendations based on numeric analyses you conduct. Please not:

1. Your recommendations are based on the information provided so NO ASSUMPTION IS REQUIRED OR ACCEPTED.
2. In offering your solution, you must show how you arrive at your decision so YOU MUST SHOW ALL YOUR WORK (what method you used, where you get the numbers from and why you are using them).
3. Giving answers without showing how your arrived at them would not receive any credit.

Holiday Baskets

Holidays Baskets is a small company that receives and deliver orders of nut baskets around Christmas times. The founder and president of this company, Helen Hemkey, needs you to help her with a couple of concerns she has been having lately.

The operations of Holiday Baskets are rather straight forward as they only take orders for 4-nuts (walnut, cashew, almond peanut) baskets, and they always have these nuts in stock. Helen receives the orders, picks the nuts in quantities ordered, places them in a bags. She then puts the bags and the shipping label in bins and sends them to the basketing workshop. In the workshop her four employees (Dianne, Nancy, Sue and Mariam) basket them, place the shipping labels on the baskets and place them on the pick-up table to be delivered to the customers by a courier company.

There are three tables in the workshop. Dianne makes her basket independently on the first table. Nancy and sue jointly work at the second table and share the work (some part of basket is completed by Nancy and then Sue finishes the basket). Mariam makes her basket independently on the third table.

Helen has built a reputation for the quality of baskets she sells to customers (the nuts are presentably sectioned and do not mix) so she does not want to have more than two percent of prepared baskets disarrayed before they are sent to the customers. She has recorded the error rates of all her employees and found that only 5% of the baskets her employees prepare might be disarrayed.

Concern 1: Would Helen be able to maintain her desired quality reputation?

Helen is also very adamant about timely delivery of her baskets to the customers. As she strives to have the next-day delivery, she uses different courier companies to deliver the completed baskets. She always asks the available courier to come and pick the completed basket from the pick-up table for delivery to the customer the next day. A typical single courier company has a 70% probability of delivering the basket the next day.

Concern 2: How many courier companies, each carrying an identical set of orders, must Helen use in order for her to have 99% confidence that the orders reach her customers the next day?