A network of railway lines connects the main lines entering and leaving a city. Speed limits, track reconstruction, and train length restrictions lead to the flow diagram below, where the numbers represent how many cars can pass per hour. Formulate an LP to find the maximal flow in cars per hour from Node 1 to Node F. Create your LP in Trab #9 1 500 300 5 2 600 400 300 400 300 3 6 7 150 200 4 500 350 200 400 300 8 9 300 600 450 500 F
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- QL (“Quebec Lumber”) is a logging and wood processing firm in a remote part of the Canadian province of Quebec. They have recently acquired a remote track of timber that is located ten miles from their processing facility. Normally, this is not a problem as they are able to simply cut the timber and haul it using trucks to their processing facility. However, this track of forestland is ten miles to their north, and there are no roads connecting the tract of land to their facility. They have also acquired a narrow (120 foot wide) ten-mile strip of land connecting this tract of timber to their processing facility. QL considered building their own road between the two points, and have log trucks haul the logs to the processing facility. However, they have decided instead to go with a less expensive option, a narrow gauge railroad. The narrow gauge railroad would require the laying of ties and steel tracks, and will require a custom-built locomotive and rolling stock (train cars that will…A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $500, how many tellers should the bank hire? (The “MMs Template with Economic Analysis” is attached for you to do the calculation. Report your input and final answer in the exam template file.)Using an M/M/1 queuing system as an example demonstrate how the event list in a simulation model would evolve over 5 discrete steps if the first part will arrive at time zero, the time between the next four arrivals are 3, 5, 6, and 4 minutes and that the machining times for the first five parts are 6, 4, 3, 5, and 4 minutes. The performance metrics of interest are the average queue length and the number of items processed.
- Please show solution and formula used. Assuming the total number of students studying in the top four universities in the Philippines is approximately 158,000. And the distribution is as follows: University of the Philippines (UP) - 40% of the total number Ateneo de Manila University (ADMU) - 23,700 De La Salle University (DLSU) - 25% of the total number University of Santo Tomas - 20% of the total number And only the following number of students owns a tablet computer: 20% of UP students 85% of ADMU students 90% of DLSU students 85% of UST students What is the total market penetration of tablet computers among the students of the top four universities? What is the total market size of tablet computers in the top four universities?HMO has 40 doctors to be apportioned among four clinics. The HMO decides to apportion the doctors based on the average weekly patient load for each clinic, given in the following table. Clinic A B C D Average Weekly 275 392 611 724 Patient Load Find the apportion of A and C using using Adam's Method. Use modified divisor 52. Doctors for clinic A Doctors for clinic B = %3D Doctors for clinic C= Doctors for clinic D =A warehouse has 2 docks for unloading. The arrival rate of trucks at the warehouse is 5 trucks per hour (Poisson distributed). The unloading rate is 4 trucks per hour (Poisson distributed). The driver- truck combination represents a cost of S275 per day. Each dock plus labor represents a cost of $900 per day. What's the minimum dock-crew and driver-truck cost (pick nearest answer)? a. 2364.10 b. 0.75 c. 1345.00 d. 2670.76 e. 0.25
- An M/M/1 queueing system has that customers arrive to it at a rate of 5 per hour, i.e., its interarrival times between two consecutive arrivals follows an exponential distribution with parameter 5 per hour. This question will ask you to evaluate two options for designing the server in the system. Both options for the single server provide the same service for the customers in the queueing system but they cost different amounts to implement. In addition, the total costs of the queuing system are the implementation costs plus the customer costs. Currently, the customer costs are $100 per hour per customer in the queueing system. In comparing these options, it costs us $100 per hour per customer in the queueing system. (a) The first option for the server is one that has a service time that follows an exponential distribution with mean 10 minutes. Determine L, W, Lq, and Wq for this system. (b) The second option for the server is one that has a service time that follows an…In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle? What is the probability of having exactly 4 customers in the system? What is the probability of having 4 or fewer customers in the system?The County Transportation Department needs to determine usage factors by day of the week for a popular toll bridge connecting different parts of the city. In the current study, they are considering only working days. Suppose that the numbers of cars using the bridge each working day over the past four weeks were (in thousands of cars) Find the seasonal factors corresponding to daily usage of the bridge.
- In an M/MA queueing system, the arrival rate is 6 customers per hour and the service rate is 8 customers per hour.Consider the following relational database for Happy Cruise Lines. It keeps track of ships, cruises, ports, and passengers. A ''cruise'' is a particular sailing of a ship on a particular date. For example, the seven-day journey of the ship Pride of Tampa that leaves on June 13, 2009, is a cruise. Note the following facts about this environment.A certain city the Transportation Authority (CTA) has trollies leaving regularly throughout the day beginning at 5:00 a.m. Although the length of a trip and the number of stops are constant, the time taken for each trip varies due to weather, traffiffiffic, and time of the day. According to the CTA, the mean time taken for the trip is 50 minutes. Suppose the travel time is Normally distributed with standard deviation σ = 4 minutes. A random sample of 25 trips is obtained, and the time for each is recorded. Find the probability that the sample mean time will be less than 48 minutes.