The Clean Pool company maintains residential swimming pools for customers in a c
ID: 448057 • Letter: T
Question
The Clean Pool company maintains residential swimming pools for customers in a city in Florida. Clean Pool has a regular maintenance schedule for all pools but also provides emergency service for customers requiring immediate help. For emergency repairs, Clean Pool has contract workers who are assigned 12 specific pools to be on call for. One such worker is Jaime who is assigned 12 specific pools in his neighbourhood; in case of a call, he would have to repair them as soon as he could. It has been found that each of these pools require emergency repair approximately once every 40 days (assume Poisson arrivals) and that repair takes ½ of a day. Jaime finds this arrangement to be stress free, except when a customer calls with an emergency and Jaime can not help them immediately (i.e. he is working on another call at the time). How often does this happen (i.e., where a customer has to wait)?
Explanation / Answer
Ans
1 Contract worker Jamie can maintain- 12 pools
Emergency Repairs - one every 40 days
One repair time - ½ day or 12 hours
If one pool require repair every 40 days we assume 365 days in a year, then 365/40 leads to 9 pools can be repaired by Jaime in one year and 40*12 = 480 days i.e. 1.5 years are required to repair 40 pools.
So now question is how often customer have to wait, it is mentioned in the question that it take half day to repair a pool so if a person calls on the same day when Jamie repairing the pools customer have to wait till end of the day to get this case done.
So Jamie repairs 9 pools in a year on approximate basis and 12 pools in 1.5 years on approximate basis, so it can happen maximum 12 times that customer have to wait for his turn when Jamie was busy cleaning pools.