Problem 3 Luna and Naomi run a pet grooming shop. Pets arri…
Questions
Prоblem 3 Lunа аnd Nаоmi run a pet grоoming shop. Pets arrive according to a Poisson process with rate . Each arriving pet is a dog with probability and a cat with probability , independently of previous arrivals. Naomi takes care of dogs only, and Luna takes care of cats only. Naomi's service time is exponentially distributed with rate dogs per hour. Luna's service time is exponentially distributed with rate cats per hour. Upon arrival of a dog, if Naomi is available, she takes care of it; otherwise, the dog leaves and does not return. Similarly, upon arrival of a cat, if Luna is available, she takes care of it; otherwise, the cat leaves and does not return. At the end of service, pets leave the shop and do not return. (a) Write down the rate matrix for a continuous-time Markov chain with state space , where means there are no pets in the shop, means there is one cat only, means there is one dog only, and means there is one cat and one dog in the shop. Is this a birth-and-death chain?(b) Let denote the state of the Markov chain at time . Find
Cаse study pаrt 1 Mrs. Singh, аge 47, was admitted tо an in-patient acute-care psychiatric unit with depressiоn. Mrs. Singh lives in a tоwnhouse in the suburb of a major city with her family, including her husband, daughter, son, and daughter-in-law. Mrs. Singh immigrated to Canada 25 years ago from northern India. She works in her brother-In-law’s restaurant as an assistant cook (chef). Her English is sufficient for carrying out the occupational therapy assessment and intervention. As the occupational therapist providing services to the in-patient acute-care psychiatric unit, you receive a referral from the unit psychiatrist to assess Mrs. Singh’s ability to return to work. Information in the client record: • This is Mrs. Singh's first admission to hospital for mental health issues. • Mrs. Singh was admitted to the unit five days ago because she expressed suicidal thoughts. • In the past several months, Mrs. Singh has had great difficulty concentrating, cries at work and has withdrawn from family activities, including cooking meals for the family. • Mrs. Singh has not worked for the past two weeks. • Mrs. Singh’s husband also works at the restaurant. He speaks limited English. • Mrs. Singh reports that she is embarrassed about being admitted to the hospital. • Mrs. Singh said, "Sometimes I have difficulty remembering things and concentrating on the task." • Co-morbidities include mild obesity. • Mrs. Singh is mobile and has no difficulties with ambulation. • Mrs. Singh’s daughter is 19 years old and is attending her first year of university. Her 24-year-old son is married and lives at home with his wife who is expecting their first child. • Medication for depression (Celexa 20 mg daily) was started three days ago. Self-Study Exercise for Part 2 Instructions: Read the additional case information below and, 1. Identify the relevant assessment data that is presented in the case study. 2. Identify the client's occupational performance issues. 3. Determine the services you would recommend for this client. You are provided 30 minutes to complete this self-study exercise. Following this, the assessor will take you through a series of oral questions related to the case. Case study part 2 As an occupational therapist you conducted your initial assessment and determined: • Mrs. Singh stated that her main goals are to: (1) Return to work at the restaurant and contribute to the household income, (2) Be a role model for her daughter, (2) Assist with chores around the house; and (3) Stop feeling sad and overwhelmed by her sadness. • Mrs. Singh was alert and oriented to person, place, and time. She was able to understand the role of occupational therapy. • Mrs. Singh was able to understand the risks and benefits of the proposed occupational therapy intervention, including the evaluation of her meal preparation skills. • Mrs. Singh speaks in a quiet tone and does not make eye contact when speaking. • Mrs. Singh reported that she can perform all self-care activities. • Mrs. Singh reported that she has been feeling sad for the past five to six months and is embarrassed about being admitted to the hospital. • Currently, Mrs. Singh is spending most of the day in bed at the hospital. • Mrs. Singh reported that at home, she feels upset when she stays in bed in the morning and leaves cooking breakfast to her daughter and daughter-in-law. She says that cooking for the family overwhelms her and prevents her from getting out of bed. • Mrs. Singh stated, "my husband is getting upset with me and is angry” because she is “embarrassing the family.” • Mrs. Singh’s usual routine involves getting out of bed at 5:00 a.m. five days a week to work as an assistant cook (chef) in her brother-in-law’s restaurant. She has been following this routine for almost 20 years. • Mrs. Singh explained that her brother-in-law was very upset with her two weeks ago because she cross-contaminated foods at the restaurant. She forgot that she had used the cutting board for raw chicken when she used it to prepare salad. All the prepared foods had to be put in the garbage. Her brother-in-law asked her to stay home until she could concentrate and be less emotional at work. Mrs. Singh has been off work for the past two weeks. • Mrs. Singh watches soap operas (drama series) on television in the evenings. She enjoys cooking and creating new menus for the restaurant and is looking forward to being a grandmother. • Home care tasks are a shared responsibility among the women of the house. The men do yard work and buy the groceries, and her husband cooks on special occasions. • Mrs. Singh values her role as a caretaker of the family. Family is very important to her, and decisions are made as a family. • Mrs. Singh does not have sick or extended health care benefits. • The family is having difficulty understanding the nature of the depression and wants to speak with the psychiatrist.