Consider an M/M/2 queueing system with arrival rate 3 and each serve with mean 0.5. Addiitonally, suppose the system has a capacity of 3 cus (a) Give the balance equations for the system. (b) Find the average number of customers in the system. (c) Find the fraction of arrivals that actually enters the system. (d) Wind the oUOROGO amount of time a customer who une oble
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- Assuming an M/M/1 system setup with a service rate of 25 entities per hour and an idling ratioof 4% Define the system’s birth rate. Define at least two ways of arriving at the number of entities in the system. Define the ratio of the time an entity spends waiting and the time the entity spends in thesystem?A line of LRT with five (5) stations will be constructed in a city. A forecast passenger demand is given below: Depart Station Boarding Station 1 2 3 4 5 1 0 1600 10000 2000 250 2 230 0 11000 2071 230 3 60 1400 0 1500 170 4 250 1700 10400 0 250 5 300 1900 12000 2500 0 (a) Compute the number of passengers between each pair of the stations for both directions.(b) In this LRT project, headway must not be less than 120 seconds and must not be greater than 300 seconds. All stations are designed to cater a train of 6 couches. The capacity of each couch is 280 passengers. Based on the computed maximum passengers in (a), compute headway possibilities and corresponding number of couches per train. You may use rail utilisation factor of 0.75 and load factor of 0.9.A fleet repair facility has the capacity to repair 800 trucks per month. However, due toscheduled maintenance of their equipment, management feels that they can repair nomore than 600 trucks per month. Last month, two of the employees were absent severaldays each, and only 400 trucks were repaired.a. Calculate the utilization of the repair shop.b. Calculate the efficiency of the repair shop.c. Discuss the utilization and efficiency of this repair facility. What can be done toimprove the operations at the facility
- It is known that in any given year, • 90% of the people in a city move to the suburbs; • 80% of the people in the suburbs do not move to the city. Given an initial city population of 55,000 and an initial suburb population of 77,000, what are the long-term population levels of the city and the suburb?The Boeing Company faces a critical strategic choice in its competition with Airbus Industries for the long-haul flight segment: Should it design and build a super-747 model that can carry 550 passengers at speeds around 350 mph, or a plane that can fly at 95 percent of the speed of sound but carry only about 350 passengers? As a member of Boeing's Planning Group, your task is to build a model to investigate the trade-offs involved in this decision.Approaching the month of Ramadan, PT Prima Sehat predicts that there will be an increase in demand for electronic goods, both TVs and microwaves. All of these electronic products have the same processing process, but have different processing times. For TV requires 4 hours of electronic processing and 2 hours of assembly. While the microwave requires 3 hours of electronic processing time and 1 hour of assembly. Of the current capacity, there is a working time for electronics as much as 240 hours, and per work time as much as 100 hours. The profit for each product is 7 (in tens of thousands) and 5 (in tens of thousands). Please use the simplex method linear programming method to solve the above case
- Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 80% of its outputs to Services and keeps the rest, while Services sells 68% of its output to Goods and retains the rest. Find equilibrium prices for the annual outputs of the Goods and Services sectors that make each sector's income match its expenditures. Denote the prices (that is, dollar values) of the total annual outputs of the Goods and Services sectors by pG and pS,respectively.A municipal solid-waste site for a city must be located at Site A or Site B. After sorting, some of the solid refuse will be transported to an electric powerplant where it will be used as fuel. Data for the hauling of refuse from each site to the power plant are shown in Table P2-4. If the power plant will pay $8.00 per cubic yard of sorted solid waste delivered to the plant, where should the solid-waste site be located? Use the city’s viewpoint and assume that 200,000 cubic yards of refuse will be hauled to the plant for one year only. One site must be selected.Suppose the number of seconds required to accelerate to 60 mph depends on both a car’s weight, its horsepower, and an interaction term between the two variables. Describe why an interaction term could be appropriate for the variables in this model and construct three linear relationships between acceleration time and weight, each for a different assumed value of horsepower.
- Cecille Paper Company uses softwood and hardwood pulp as basic materials for producing converter-grade paper. Hardwood is 80% pulp fiber and 20% pulp binder, while softwood is 50% pulp fiber and 50% pulp binder. The cost per pound for hardwood and softwood is $.50 and $.40, respectively. The company s quality control expert specifies that in order for the product to meet quality standards, each batch must contain at least 12,000 pounds of pulp fiber and at least 6,000 pounds of pulp binder. Because of equipment limitations, the size of a batch cannot exceed 24,000 pounds. The Production Department recently received a new standard from the Cost Department, allowing $8,200 per batch. The production manager feels that this amount is too low, because such costs have never been less than $8,400. Required: Using the graphic method, determine the hardwood and softwood mix necessary to minimize the cost per batch.A Manufacturing Corp. with three-station work cell has the process displayed below. Each workstation has only one worker to the assigned activity. Single order arrives every 7.5 hours. c) What is the cycle time corresponding to maximum throughput and actual throughput?d) Suppose that a second parallel machine is added at station 2. What is the new bottleneck timeand new throughput time of the system? How did the addition of the second machine at workstation 2 affect the performance of the work cell? IN Station 1 OUTTask Time: 3 hrs.Station 2Task Time: 5 hrs.Station 3Task Time: 2 hrs.A private investment club has $200,000 earmarked for investment in stocks. To arrive at anacceptable overall level of risk, the stocks that management is considering have been classifiedinto three categories: high risk, medium risk, and low risk. Management estimates that high-riskstocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks,6%/year. The members have decided that the investment in low-risk stocks should be equal tothe sum of the investments in the stocks of the other two categories. Determine how much theclub should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment. (Assume that all the money available for investment isinvested.)Note: Develop the linear system of equations from the above theory and solve the system byGauss Jordon Method.