Waiting line problems : give me please results of calculation (results not only methods I want to make sure that my answers are accurates) and define the model we will use for each problem (1, 2 or 3)

1- The Sycamore & Sam law firm produces many legal documents that must be typed for clients and lawyers in the firm. Requests average 12.5pages of documents per hour, and they arrive according to a Poisson distribution. The time to type a page depends on the complexity of the documents, but averages 4.2 minutes per page. Completed pages are immediately transferred to a pickup station which notify the appropriate user that the documents are ready. a) What is the average utilization rate of the secretary? b) What is the probability that more than 4pages are waiting or being typed? c) What is the average number of pages waiting to be typed? d) What is the average time a document will be sitting at the secretary station?

2) The Savoir Faire Resort is a new (and somewhat pretentious) hotel that uses latest technology as part of their competitive advantage strategy and also to increase productivity. Their Bougie Bar features several hi-tech service options including a Nestl automated espresso drink dispenser. This machine has proven to be a big hit with the Bougie clientele. On average, 22 guests will use the machine each hour, and the machine spends exactly 1.5 minutes preparing and dispensing the requested beverage. Given this information: a) How long will an average guest have to wait in line before having their chance to select their yummy beverage? b) On average, how many guests will be at the machine (both using the machine and waiting their turn)? c) What percent of the time is the machine busy servicing guests? d) Some clientele have expressed a little more customization so the manager is considering replacing the machine with a human barista. The barista would take 2.2 minutes on average to make a drink, but of course the time would vary based on the particular order. i) Will this change be feasible given the demand on the system? ii) If yes, what would be the average time a customer would wait under this new system?