A certain lady owns a salon and currently runs it alone. Customers arrive at a salon according to a Poisson process with mean arrival time of 20 minutes. Customers spend an average of 15 minutes in...

A certain lady owns a salon and currently runs it alone. Customers arrive at a salon according to a Poisson process with mean arrival time of 20 minutes. Customers spend an average of 15 minutes in the hairdresser's chair. (??) What is the expected number of customers in the salon and in the queue?


Assignment 2 Operations Research 3 (OPR360S) 2021 Marks: 61 Due Date: 30 September 2021 Instructions: • Answer all the questions and write your answers clearly and legibly. • Convert your work to a single pdf document and submit via blackboard. • The first page must bear you name, surname, student number & subject name. Question 1 [6 + 4 + 3 + 3 + 3 + 3 + 3 = 25 marks] A certain lady owns a salon and currently runs it alone. Customers arrive at a salon according to a Poisson process with mean arrival time of 20 minutes. Customers spend an average of 15 minutes in the hairdresser's chair. (?) What is the expected number of customers in the salon and in the queue? (??) Calculate the % of time an arrival can walk straight into the hairdresser 's chair without having to wait? (???) How much time can customers expect to spend in the salon? (??) What is the average time customers spend in the queue? (?) What is the probability the waiting time in the system is greater than 35 minutes? (??) Calculate the % of customers who must wait prior to getting into the hairdresser's chair. (???) What is the probability that more than 3 customers are in the system? Question 2 [5.5 + 11 + 5.5 + 14 = 36 marks] The following are the precedence requirements, normal and crash activity times, and normal and crash costs for a construction project Activity Precedence activities Normal time in weeks Crash Time in weeks cost Normal Cost in rands Crash cost in rands ? − 5 3 8000 10 000 ? ? 4 2 7 000 8 000 ? ? 2 1 5 000 6 000 ? ?, ? 5 2 9 000 12 000 ? ?, ? 1 1 8 000 10 000 ? ? 3 2 6 000 8 000 ? ?, ? 4 1 10 000 22 000 ? ?, ? 4 2 9 500 11 000 (?) Construct the project network for the above activities. (?) Perform a forward and backward pass and hence find the project completion time and the critical path(s). (?) Find the total float of all the activities and hence determine activities which can be delayed without affecting the project completion time. (?) To shorten the project by 3 weeks, which tasks would be shortened and what would the final total project cost be? GB/OPR/ass2/2021