Problem 1113 (Algorithmic) Pete's Market is a small local grocery store with onlyr one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 15 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the Following alternatives for improving service. Calculate the value of Wq for each alternative. a. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 30 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. in. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 20 customers per hour For each server. Note: Use Pu values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. What alternative would you recommend? Justify your recommendation. Recommend =one checkout-counter with-two em "I6 ees '-= J , The two counter system hos-better- sei'v'ic'e hutcosts r'iri'd'r'i; ' v J . Problem 11-15 (Algorithmic) Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution, with an arrival rate of seven calls per hour. On average, it takes 7.5 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution. To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. What effect would the additional consultant have on customer service? Would two technical consultants enable Ocala to meet its service guidelines (no more than 35% of all customers having to wait for technical support and an average customer waiting time of two minutes or less)? Round your answers to two decimal places. With two consultants, 87.5 X % of customers have to wait, with an average waiting time of 52.5 X minutes. Therefore, two consultants meet V service goals. Feedback Check My Work Partially correctProblem 1119 (Algorithmic) All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 4 passengers per minute. On Monday morning the arrival late is 7.8 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. when the security level is raised to high, the service rate for processing passengers is reduced to 3 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. a. The facility manager's goal is to limit the average number of passengers waiting in line to 4 or fewer How many screening stations must be open in order to satisfy the manager's goal? Having 3 ' VI station(s) open satisfies the manager's goal to limit the average number of passengers in the waiting line to at most 4. b. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places. X minutes Problem 1121 (Algorithmic) Agan Interior Design provides home and office decolating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan's management would like to evaluate two alternatives: - Use one consultant with an average service time of 8 minutes per customer. - Expand to two consultants, each of whom has an average service time of 10 minutes per customer. If the consultants are paid $19 per hour and the customer waiting time is valued at $28 per hour for waiting time prior to service, should Agan expand to the twoiconsultant system? No 'J What is the total cost for each scenario? Round your answers to the nearest cent. The total cost for the rst scenario where there is one consultant with an average service time Di 8 minutes per customer is $ X . The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $ | Note: Use Pg values from Table 11.4 to answer the questions below. Problem 11-31 (Algorithmic) Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour. a. How many extension lines should be used if the company wants to handle 85% of the calls immediately? X lines should be used b. What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places. L = 0.05 X c. What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal places. 10 %TABLE 11.4 VALUES OF P. FOR MULTIPLE-SERVER WAITING LINES WITH POISSON ARRIVALS AND EXPONENTIAL SERVICE TIMES Number of Servers (k) Ratio ALL 2 3 4 5 0.15 0.8605 0.8607 0.8607 0.8607 0.20 0.8182 0.8187 0.8187 0.8187 0.25 0.7778 0.7788 0.7788 0.7788 0.30 0.7391 0.7407 0.7408 0.7408 0.35 0.7021 0.7046 0.7047 0.7047 0.40 0.6667 0.6701 0.6703 0.6703 0.45 0.6327 0.6373 0.6376 0.6376 0.50 0.6000 0.6061 0.6065 0.6065 0.55 0.5686 0.5763 0.5769 0.5769 0.60 0.5385 0.5479 0.5487 0.5488 0.65 0.5094 0.5209 0.5219 0.5220 0.70 0.4815 0.4952 0.4965 0.4966 0.75 0.4545 0.4706 0.4722 0.4724 0.80 0.4286 0.4472 0.4491 0.4493 0.85 0.4035 0.4248 0.4271 0.4274 0.90 0.3793 0.4035 0.4062 0.4065 0.95 0.3559 0.3831 0.3863 0.3867 1.00 0.3333 0.3636 0.3673 0.3678 1.20 0.2500 0.2941 0.3002 0.301 1 1.40 0.1765 0.2360 0.2449 0.2463 1.60 0.1111 0.1872 0.1993 0.2014 1.80 0.0526 0.1460 0.1616 0.1646 2.00 0.1111 0.1304 0.1343 2.20 0.0815 0.1046 0.1094 2.40 0.0562 0.0831 0.0889 2.60 0.0345 0.0651 0.0721 2.80 0.0160 0.0521 0.0581 3.00 0.0377 0.0466 3.20 0.0273 0.0372 3.40 0.0186 0.0293 3.60 0.0113 0.0228 3.80 0.0051 0.0174 4.00 0.0130 4.20 0.0093 4.40 0.0063 4.60 0.0038 4.80 0.0017