In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 85% chance that she will be at work tomorrow,and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 740 employees at work. (A graphing calculator is recommended.)(a) Find the transition matrix A for this scenario.at workabsentA =(b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.)employees(c) Find the steady-state vector x. (Round your answer to two decimal places.)

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Answered: In an office complex of 1000 employees,…

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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A car rental company has two locations. Each week, 80% of the cars rented at location A are returned to location A and the rest location B. Of the cars rented at location B, 30% are returned to location B by the end of the week and the rest to location A. a. Make a transition diagram for this process. b. Write the transition matrix T for this process. cIf 50% of the company's cars start this week at location A, and 50% at location B, find the proportion of cars that will be at each location one week later Label your answers. d. Write and solve a system of equations to find the stable distribution (correct to 3 decimal places) for this Markov process. Show all calculations and label the row operations.
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Answer all parts of question 3
(a) Create a graph with six vertices of degrees 2, 2, 2, 3, 4 and 5. Construct the matrix of the graph you created. Show your results clearly.(b) Create a graph with six vertices of degrees 0, 2, 3, 4, 5, and 6. Construct the matrix of the graph you created. Show your results clearly.(c) Create a graph with six vertices of degrees 0, 1, 2, 3, 4, and 5. Construct the matrix of the graph you created. Show your results clearly.
Question 1. JoJo Mobile sells data plans for cellphones. They sell Individual Plans as well as Family Plans. Market analysts at JoJo Mobile have noticed that customers tend to switch between the two plans each year. . Among the customers with an individual plan, 30% switch to a family plan the next year. . Among the customers with a family plan, 20% switch to an individual plan in the next year. This information can be encoded into a 2 x 2 matrix, as follows: [0.7 0.2] [0.3 (a) Compute the vector P-¹ (b) The vector P³ 3 740 650 400 600 P = 0.3 0.8 and give a physical interpretation of what this vector represents. and give a physical interpretation of what this vector represents. (c) An eigenvector for P with eigenvalue λ = 1, and give a physical interpretation of what this vector represents. (d) An eigenvector for P with eigenvalue > < 1. Explain why the eigenvector does not have a physical interpretation.
A car rental service in a certain town has a fleet of about 600 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix to the right. Suppose that on Monday there are 295 cars at the airport (or rented from there), 65 cars at the east side office, and 240 cars at the west side office. What will be the approximate distribution of cars on Wednesday? Cars Rented From: Airport East West 0.95 0.03 0.12 0.00 0.94 0.06 0.05 0.03 0.82 Returned To: Airport East West On Wednesday, 274 cars will be at the airport, 52 cars will be at the East location, and 274 cars will be at the West location. (Round to the nearest integer as needed.)
29. In a fictional town, there are two restaurants, which we will call A and B for ease of reference. If someone eats at restaurant A on one day, there is a 76% chance they will eat there again tomorrow. And if someone eats at restaurant B on one day, there is a 82 % chance they will eat there again tomorrow. Which one of the transition matrices below correctly represents this situation? a) A B A 0.76 0.34 B 0.18 0.82 b) A B A 0.76 0.24 B 0.18 0.82 c) A B A 0.76 0.24 B 0.08 0.82 d) A B Main Content A 0.24 0.76 B 0.82 0.18 e) None of the above.
Please solve and show soution for question 2
2. Find the adjacency matrix for the following graph. d G7

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