1 The cost of waiting is estimated to be about an average of $20 per hour. Each pump cost about $11000 per year for the maintenance fee and investment loan interests. Assuming 365 days a year and 12 hours per day. Determine how many new pumps need to be installed to minimize the expected total cost per hour. If no new pumps need to be installed, answer 0. 60 customers per hour (mean arrival rate) and 15 customers per hour (mean service rate)
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The cost of waiting is estimated to be about an average of $20 per hour. Each pump cost about $11000 per year for the maintenance fee and investment loan interests. Assuming 365 days a year and 12 hours per day. Determine how many new pumps need to be installed to minimize the expected total cost per hour. If no new pumps need to be installed, answer 0. 60 customers per hour (mean arrival rate) and 15 customers per hour (mean service rate)
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- Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.Explain how waiting lines can develop even when the service time is a constant.The vehicles are entering the parking area of the a mall.There is only one ticket line to get and pay a parkingticket. Each ticket purchase takes an average of 18seconds. The average arrival rate is 3 vehicles/minute.Find the average length of queue, average waiting timein queue and average time spent by the vehicles in thesystem assuming M/M/1 queuing.
- is queuing theory Five drilling machines at Al Hamriya steel is maintained by Lumina maintenance service with 2 service Engineers. The drilling machines require Maintenance at the of 20 per hour. The engineers fix machine in 2.4 mins every time it goes out of service: 1. What is the probability that no drilling machine needs service ?Patients arrive at a dentist’s office with an arrival rate of 2.8 patients per hour. The dentist can treat patients at a service rate of 3 patients per hour. A study of patient waiting times shows that a patient waits an average of 30 minutes before seeing the dentist. Note the M/M/1 model does not necessarily apply here. What are the arrival and service rates in terms of patients per minute? What is the average number of patients in the waiting room? If a patient arrives at 10:10am, at what time is the patient expected to leave the office?Western National Bank wants to provide a drive-through window for its customers. Management estimates that customers will arrive in their cars at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of 20 per hour. Assuming Poisson arrivals and exponential service, find the following: Capacity utilization of the teller. Average number of cars in the waiting line Average number in the system. Average waiting time in line. Average waiting time in the system, including service.
- One mechanic services 6 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 3 working days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of one repair job per day. Repairs follow a negative exponential distribution. a) On the average, how many machines are waiting for service? The average number of machines waiting for service is12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service? d. What is the average number of cars in line behind the customer receiving service? e. What is the probability that there are no cars at the window? f. What percentage of the time is the postal clerk busy? g. What is the probability that there are exactly two cars in the system?Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copierrepairs come in at a mean rate of three per eight-hour day (assume Poisson).A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?D) What is the average number of customers awaiting repairs?
- One mechanic services 7 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 8 working days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of three repair jobs per day. Repairs follow a negative exponential distribution. a) On the average, how many machines are waiting for service? The average number of machines waiting for service is. Round your response to three decimal places.) B.) The average time in the system C.) The average number in lineC) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) +…Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ?customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places).