please do not do problem-1. will need answer by 5pm

Problem-2 The manager of the Radford Credit Union (RCU) wants to determine how many parttime tellers to employ to cover the peak demand time in its lobby from 11 am to 2 pm. RCU currently has 3 full-time tellers, but during this peak demand time customers have been complaining that the wait time for service is too long. The manager at RCU has determined that customers arrive according to a Poisson distribution with an average of 60 arrivals per hour during the peak period. Each teller services customers at a rate of 24 per hour also Poisson distributed. Customers wait in a common line. a. On average, how long must customers wait in line before service begins? b. Once service begins for a customer, how long does it take on average to complete the transaction? c. What percentage of the time are all three servers tellers busy? d. What percentage of time are there more than 5 customers waiting to be served? e. If one part-time teller is hired to work during the peak time period, what effect would it have on the average amount of time a customer waits in queue? f. With this part-time teller, what is the average number of people in line? g. With this part-time teller, what is the probability that an arriving customer will not have to wait for service? Problem-3 The Austin City Marathon takes place in Austin, Texas each April. The organizers of this race are trying to solve a problem that occurs at the finish line each year. Thousands of runners take part in the race. The fastest runners finish in a little over 2 hours, but the majority finish about 1.5 hours later. After runners enter the finish area, they go through one of four finish chutes where their times and places are recorded. Each chute has its own queue. During the time in which the majority of the runners finish the race, the chutes become backlogged and significant delays occur. The organizers want to determine how many chutes should be added to eliminate this problem. At the time in question, runners arrive at the finish area at a rate of 50 per minute according to a Poisson distribution and they randomly select one of the queues to join. Once they join the queue they have to stay in that queue until they get served. The time required to record the necessary information for each finishing runner at any chute is exponentially distributed with a mean of 4 seconds. a. Under the current arrangement with four chutes, what is the expected length of the queue at each chute? b. What is the expected number of people waiting in the finish area to have their times and places recorded? c. Under the current arrangement what is the average amount of time that a runner waits before being processed? d. What is the probability that a chute will be idle? e. What is the probability that all four chutes will be idle at the same time? f. How many chutes should the organizers add if they want to reduce the queue time at any chute to an average under 5 seconds? Problem-4 Answer all the questions in Problem-3, but now assume that runners are made to stand in one line when they arrive. When a chute becomes free, the first person in line walks over to it to record his/her time and place. Problem-5 Regal Department Store runs a large warehouse to receive the merchandise that it then distributes to all its retail stores. Trucks arrive at this warehouse following a Poisson distribution with a rate of one very 5 minutes. Seven loading docks are available at the warehouse. A single worker runs each dock and is able to unload a truck in about 30 minutes on average, exponentially distributed. When all docks are occupied, arriving trucks wait in a queue until one becomes available. Regal has received several complaints from the trucking companies about how long it takes to unload. In response, Regal is considering a number of options. One option is to hire an extra worker for each unloading dock. This is expected to reduce the average time it takes to unload a truck to 18 minutes, exponentially distributed. It costs approximately $25 in salary and benefits to employ each additional worker. Alternatively, Regal can continue to use a single worker, but upgrade the forklift equipment workers use to unload the trucks. The company can do this at an extra cost of about $30/hour and is expected to reduce the unloading time to about 23 minutes on average, again exponentially distributed. Finally, the company can build two new loading docks for a capitalized cost each of $22 per hour and hire two additional workers at a rate of $$25 per hour each to run these two new locations. Regal estimates that making a truck wait costs it $100 per hour in lost goodwill. Which, if any, of these alternatives should it implement