Original Problem: Denmark, LLC, is a large packaged food company focused on developing, manufacturing, marketing, selling and distributing baked sweet goods in the Nothern Europe. Denmark Logistics, a Denmark LLCs subsidiary, is in charge of distribution and employs one team to load baked sweet goods on outgoing company trucks in a 8 working hour shift per day. Trucks arrive at the loading gate at an average of 24 per day, according to a Poisson distribution. The worker loads them at a rate of 32 per day, following the exponential distribution in service times. Truck drivers and team loaders working for Denmark Logistics are paid at $13.5 and $8.8 per hour on average, respectively. Since truck drivers waiting in the queue are drawing a salary but are productively idle and unable to generate revenue during that time. Scenario 1: Denmark Logistics considers that adding a second fruit loader team will substantially improve the distribution efficiency. They estimate that a two-team crew, still acting like a singleserver system, at the loading gate will just double the loading rate. Scenario 2: Denmark Logistics considers that building a second platform to speed up the process of loading their sweet goods trucks. Assume that the arrival rate and service rate dont change as before building an additional platform. 1. Determine the appropriate queue models and operating characteristics of the loading gate of the original problem and Scenerio 1 and 2. Operating characteristics are values of average waiting times, average number of trucks, utilization factor, 2. Calcualte probabilities in the original problem and Scenerio 1 and 2 a. What is the probability that there are no trucks either being loaded or waiting?b. What is the probability that there are exactly two trucks either being loaded or waiting? c. What is the probability that there will be more than three trucks either being loaded or waiting? 3. Should Denmark Logistics add an additional loader (Scenario 1) or remain 1 team loader (Original problem)? What would be the cost savings since employing two team loaders instead of one? 4. Should Denmark Logistics build an additional platform (Scenario 2) or remain 1 platform (Original problem)? What would be the cost savings since building an additional platform? 5. Should Denmark Logistics add an additional loader (Scenario 1) or build an additional platform (Scenario 2) or doing nothing (Original problem)?