Suppose customers arrive to a single server at the rate of 1/2 customers per minute. The capacityof the server is 1/3 customers per minute. Both service time and interarrival times are assumedto be exponential. Suppose the system is initially empty. As the system unfolds, its inventory (inprocess and waiting) will:(a) reach a long-run average of 3 customers(b) reach a long-run average of 2 customers(c) stay in the system an average of 6 minutes(d) grows unboundedly in the long-run(e) None of the above

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Answered: Suppose customers arrive to a single…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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in 2017, the residents of eugene were producing greenhouse gas emissions at an average rate of 16 tons of co2 per resident per year, and that the amount was decreasing at an instantaneous rate of .22 tons per year. however the population of euegene was 170,000 and growing at a rate of 2,000 people per year. at what instantaneous rate was the total greenhouse gas emissions in eugene growing in 2017 ?
Suppose demand is given by p = 1600 − x. Find the maximum revenue.
Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?
(ii) A state predicts that it will need $2.15 billion for construction of new roads and maintenance of existing roads in year 2025. It is forecast that 1.5 percent of the vehicle-fleet in that year will be electric vehicles with the remaining being gas powered vehicles. The population of the state is forecast to be 10 million persons in 2025 with the average number of vehicles owned per person being 0.75. It is projected that on average each vehicle will be driven 12,000 miles per year, with gas powered vehicles achieving an average gas consumption of 25 miles per gallon (mpg). If the state plans to raise 99 percent of the required revenue from gas powered vehicles and the remainder from electric vehicles, (a) Determine how much each gallon of gas sold should be taxed to achieve the revenue target (b) Determine what the annual flat tax for each electric vehicle should be to raise the appropriate revenue target; (c) If the state decides to raise the required revenue based on a tax per…
Example 12.8. A firm uses milling machines, grinding machines and lathes to pro- duce two motor parts. The machining times required for each part, the machining times avail- able on different machines and the profit on each motor part are given below : Machining time reqd. for the motor part Max. time available per Type of machine (mts) week (minutes) I II 10 2,000 Milling machines Grinding machines Lathes. 2 900 12 3,000 Profit/ unit (Rs.) 100 40 Determine the number of parts I and II to be manufactured per week to maximize the profit. د ه
Two competing companies produce mobile phones. Company A starts production at 1000 phones per week and plans to increase output by 200 each week. Company B starts production with 500 phones per week and plans to increase output by 20% each week. (a) Calculate the weekly production in weeks 1; 5; 10; 15. Plot the graph of weekly output for each producer on the same diagram (use Excel, if available). Estimate the week in which the output is the same for both firms. (b) Calculate the total production during the first 15 weeks for each firm.
How does time-period or length of run affects the behavior of the supply function?
Replace the March demand forecast 510 by C. During a 46-day period when there were 120 workers, the firm produced 1,700,000 cookies. Assume that there are 100 workers employed, and C cookies in inventory at the beginning of month 1 (January). Further assume that the inventory carrying cost cI = $0.10/cookie/month, employee hiring cost cH = $100/work, and cost of firing one worker cF = $200/worker. It is required that the inventory level at the end of month 12 (December) is 2C. use the Constant workforce plan (level strategy): Find the minimum constant workforce needed to meet all monthly demands (i.e, back order not allowed). Computer the total cost including employee hiring or firing cost (which occurs only at the beginning of month 1), and inventory carrying cost.
A person wants to earn the profit of $200,000 from his three goods next year. Product A gives him a profit of $100 and has an expected growth of 10% per year. Product B provides a profit of $200 and has an expected growth of 5% per year. Product C provides a profit of $150 and has an expected growth of 8% per year. The person plans to sell two times of product C as of product B. If the person estimated a total growth of 12% per year in his profits, how many of each product should the person sell in a year? the answer is A: 1931, B: 14, C: 28

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