Concerned about their cooling system not working properly, the four partners argue about how these orders should be handled. Mary insists that the orders should be handled in the same order they have been feceived. Nancy argues that they should handle the orders that can be done faster first and then move to ones that take longer to be completed. Sandra insists they should finish orders that are due earlier.

Listening to her partners' arguments, Julie who is mature and experienced with business operations invited them to calm down and said: $*$since we have other finished orders in the kitchen, we have room for limited number of jobs on the go$.$

Wedding cakes are delicate and we need to have the space to do the ordered details.

So I suggest we look at the average number of wedding jobs in the kitchen to decide whose suggestion would generate the best flow in the kitchen." The other partners agreed because they believed Julie speaks with operation experience. Julie is also very adamant about timely delivery of cakes to the customers so she uses different courier companies to deliver the completed orders. The courier companies work in parallel and each of them has a $80\%$ reliability for delivering the basket the on time.

a$-$Whose suggestion $($Mary$\text{'}$s$.$ Nancy's or Sandra's$)$ do you pick and why? $[15$ marks$]$

b$-$ 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 on