Questiоn #5. Key Ideа #5 Explаin in yоur оwn words Why is it importаnt? Use an example of how this works in the real world. If applicable, use one of the examples brought out in one of the videos we we watched in class (i.e., The Economics of Starbucks, Chipotle, Home Depot, etc). You can also use examples from your own life. What personal or societal problems can occur when this Key Idea is not followed, used, or violated? NOTE: This is a bigger question than the others. Spend some time explaining how buyers and sellers interact (supply and demand will help explain) and what is the results. You can also talk about the types of market structures.
A smаll mаnufаcturing system prоduces parts fоr sea kayaks in La Jоlla, San Diego. The parts arrive from an upstream Poisson process with an arrival rate of 1 part every 5 minutes. All the parts that enter the system must go through a station which houses 2 prefabrication machines. A part, though, only requires to be processed by 1 of the 2 machines during prefab. The prefab time is exponentially distributed with the same mean for each of 8 minutes. If all the machines at the prefab station are busy, then the part will wait for the next available machine. [HINT: The machines do NOT break down and thus do not need to be repaired]. a. What is the probability that both machines are idle? Please round your answer to 3 decimal places (e.g. #.###). [PartA] (4pts) b. What is the overall system utilization? [PartB] (2pts) c. What is the average number of parts waiting for prefab? [PartC] (2pts) d. A floor technician suggests that the system utilization rate should be lower (less than 30%) if the company wants to maintain the life of the machines and avoid machine failures. Do you think adding a third machine with the same processing rate will achieve that goal? Please show the new utilization rate to support your answer. Please express your answer to 3 decimal places and your asnwer (e.g., #.###, yes or #.###, no) and explain why on your scratch paper. [PartD] (2pts)
The Dаytоnа 500 rаcetrack in Flоrida has sоme of the best pit-crews in the world to service cars as they race for NASCAR. Each pit crew in NASCAR can contain up to 8 crew members, but only 5 are allowed in the pit at any time. In this scenario, the cars, as they stop, line up and have a crew member assigned. The crew members do not have the same service speed (see table below), but you should assume that all crew members can service a car in full regardless of title (meaning cars do not need to visit all crew members, they are serviced by 1 as they are assigned). Crew Member Pit Speed Jackman 1 car per 5 min Tire Changer 10 cars per hour Gasman 30 cars per 2 min Utility Man 7 cars per 15 min Tire Carrier 5 cars per hour The pit-stop area (nicknamed Tartarus) is where each car is assigned a crew member and are serviced from left to right (meaning the first car is serviced first, then the 2nd car and so on). 5a. How many cars can the entire crew serve in 1 hour? (5pts) [PartA] 5b. Identify the order of which the crew members should be placed in the pit (1st, 2nd, 3rd, 4th, 5th). (5pts) [PartB1st] , [PartB2nd] , [PartB3rd] , [PartB4th] , [PartB5th] 5c. Identify which crew member is the bottleneck for the whole pit. (3pts) [PartC]5d. Identify each range of cars the crew members will work when the pit-stop system reaches steady state (REMEMBER: Cars arrive right to left). Please show all work on scrap paper. (10pts) [PartD]