and 50 weeks/year. Calculate the availability of a machine. Calculate the expected number of machines in running condition if we visit the facility at a random time (hint: recall the Little's Law approach). Calculate the total expected cost of repairs on all machines per year and the total expected cost of downtime of all machines per year.
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- no handwritten solution Question The management of a busy petrol station is concerned that customers are being lost because of long waiting times sometimes required at their petrol pump. Over a two weeks period a careful study has been taken of the arrival of cars and the length of time taken to serve customers at the petrol station. The tables below show the arrival rates and the service time distribution: Inter arrival time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <2 1 60 60 00 - 59 2 - <4 3 25 85 60 - 84 4 - <6 5 10 95 85 - 94 6 - <8 7 5 100 95 - 99 Service time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <4 2 20 20 00 – 19 4 - <6 5 30 50 20 – 49 6 - <8 7 20 70 50 - 69 8 - <10 9 15 85 70 – 84…Problem 2-4 (Algo) A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 5 workers, who together produced an average of 80 carts per hour. Workers receive $12 per hour, and machine cost was $30 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $11 per hour, while output increased by 5 carts per hour. a. Compute labor productivity under each system. Use carts per worker per hour as the measure of labor productivity. (Round your answers to 3 decimal places.) Before After b. Compute the multifactor productivity under each system. Use carts per dollar cost (labor plus equipment) as the measure. (Round your answers to 3 decimal places.) Before After carts per worker per hour carts per worker per hour Labor productivity…Problem 15-31 (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.
- The Corner Cleaners 24-hour laundromat has 16 washing machines., A machine breaks down every 20 days (exponentially distributed). The repair service the laundromat contracts takes anaverage of one day to repair a machine (exponentially distributed). A washing machine averages $5 per hour in revenue. The laundromat is considering a new repair service that guarantees repairs in 0.50 day, but they charge $10 more per hour than the current repair service. Currently, how long does the laundromat have to wait for its equipment to be repaired? days, (Round your answer to 2 decimal places, the tolerance is +/- 0.05.) What is the cost of equipment downtime? | (Round your answer to 2 decimal places, the tolerance is +2.5) %241. Apple Computer Inc. bought $900 of materials from its vendor for athe particular order of 6 computers. To deliver this particular order, UPS driver needs to stop in 3 different places to cover a total distance of 550 miles, the cost per stop is $0.58 and the cost per mile is $0.35 since it is using UPS service for delivery. Marginal cost per stop is $0.30, the fixed cost of handling a pallet of computers (pallet size = 6) is $12 and the variable cost of handling the same pallet is $6.60.a. How much Apple should charge a customer for shipping and handling for each computer?b. Find shipment cost for this order.c. Find the total cost per computer if Apple holds its inventory on an average 1.5 months at $0.75/year against every $1 of inventory?1. A multiple channel queuing system with a Poisson arrival rate, and an exponential service time distribution has an average arrival rate of 2.5 customers per hour and an average service time of eighty minutes per customer. A queuing system is described as unstable or overloaded if its utilization rate is greater than, or equal to one. For the system just described, what is the minimum number of servers required to retain stability i.e., to avoid overloading? A. 2 B. 3 C. 1 D. 4
- Q2. Customers visit an astrologer at a rate of 4/hour (Poisson) and take and average of 12 minutes (Exponential). Compute the probability that: a) There are three or less people in the system b) There are 5 or more people in the system c) The astrologer is freeQ2. In Aegis life insurance company, the deposit and withdrawal functions associated with cer- tain investment product are separated by two clerks, Stack and Slack. Deposit slips arrive at Stack’s desk according to a Poisson process with a mean rate of 16 per hour. Withdrawal slips arrive at Slack’s desk according to a Poisson process with a mean rate of 14 per hour. The time required to process either transaction has an exponential distribution with a mean of 3 minutes. Based on this information, answer the following questions: (a) In the current situation, what model will you apply for analysis of queuing system at Stack’s desk and Slack’s desk? Answer this question by filling the following table. Model λ µ ρ Reaches steady state? Stack's Desk - - - - - Slack's Desk - - - - - (b) What is the expected waiting time of a deposit slip at Stack’s desk? What is the expected waiting time of a withdrawal slip at Slack’s desk? Suppose “the system” contains both Stack and…The Corner Cleaners 24-hour laundromat has 16 washing machines. A machine breaks down every 20 days(exponentially distributed). The repair service the laundromat contracts takes an average of one day to repair amachine (exponentially distributed). A washing machineaverages $5 per hour in revenue. The laundromat is considering a new repair service that guarantees repairs in0.50 day, but they charge $10 more per hour than thecurrent repair service. Should the laundromat switch tothe new repair service?
- Problem 3-5 (Algo) Best Bicycles manufactures three different types of bikes: the Tiny Tike, the Adult Aero, and the Mountain Monger. Assume that Best Bicycles operates two shifts, each with 1,750 hours per year. Bike Tiny Tike Adult Aero Mountain Monger Demand Porecast Processing Time (minutes/unit) 29.3 23.8 15.3 (units/year) 45,630 44,800 24,800 Lot Size (# of bikes) 26 26 32 Setup Time (minutes/setup) 52 82 48 pictureClick here for the Excel Data File PLEASE NOTE: The Excel file shows the column C values for Processing time rounded to a whole minute. You'll get the answer wrong If you use this rounded value. In Excel, select cells C3 to CS and on the Home ribbon, in the Number section, click the Increase Decimal button. Calculate the required capacity for this year's production. Note that the times are given for assembly lines, so capacity calculations should be in terms of the number of lines necessary. (Round up your answer to the next whole number.) Number of assembly linesCapacity Service Rate Number of Servers Capacity Service Rate Number of Servers 120 12 10.00Problem 11-19 (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 3 passengers per minute. On Monday morning the arrival rate is 5.2 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 2 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. The facility manager's goal is to limit the average number of passengers waiting in line to 10 or fewer. How…