2 Question 2: Consider a manufacturing facility with 28 machines. These machines, on average, after beingrepaired work for 180 hours and take 9 hours to repair. Each repair costs 250 TL/repair. The hourly cost of amachine being repaired (downtime cost) is 300 TL/repair. The facility operates 10 shifts/week, 8 hr/shift,and 50 weeks/year. Calculate the availability of a machine. Calculate the expected number of machines inrunning condition if we visit the facility at a random time (hint: recall the Littles Law approach). Calculatethe total expected cost of repairs on all machines per year and the total expected cost of downtime of allmachines per year.Availability =ex: 78.4%Expected Num ofMachines Runningex: 42.6Total ExpectedCost of RepairsTL/yrex 210943TL/yrTotal ExpectedCost of Downtimeex 353670

Answered: Image /qna-images/answer/aa19862b-225e-4180-b467-91ba0a79d8c7.jpg

Answered: and 50 weeks/year. Calculate the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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QUESTIONS: 1. A refiner in city Q serves four customers near city W and maintains consignment inventory (owned by the refiner) at each location. Currently, the refiner uses TL (truckload) transportation to deliver separately to each customer. Each truck costs $(759) plus $(309) per stop. The refiner is considering aggregating deliveries to city W on a single truck. The demand of the first customer is 75 tons a year, the demand of the second customer is 30 tons per year, and the demand of the third and fourth customers is 10 tons per year. The product cost is $8,000 per ton, and it uses a holding cost of (24)%. The truck capacity is 20 tons. a. What is the optimal delivery policy to each customer if the refiner ships separately to each of them? What is the annual total inventory-related cost? b. What is the optimal delivery policy to each customer if the refiner aggregates shipments to each of the four customers on every truck that goes to city W? What is the annual total…
Question 3: A catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem. Part B: Use Excel Solver to solve the problem (provide exact values for all variables and the optimal objective function).
Question 2 A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N ) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a+bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. the number of drivers that join the road is Ne = (v−a)/b (iv) Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others.
Question 1The Rotary Club is holding a pizza sale to finance outreach projects. The Club made an agreement to purchase pizza from Pizza Hut at a 30% discount which the Rotary Club can then resell for a profit. It is expected that of the 500 families in the community, at most 70% will buy pizza. Based on a survey of their personal preferences, the students believe that they should orderno more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. They also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. The standard price (before discount) for the cheese, pepperoni and vegetarian is $12, $15 and $14, respectively. The Rotary Club makes a profit of 10%, 15% and 20%, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. a) Formulate a linear programming model that would determine the optimal solution. An explanation for the derivation of EACH equation should…
Question #4 - Jerry Smith is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a 5-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry is also thinking about hiring his old marketing professor to conduct a marketing research study. If the study is conducted, the study could be favorable (i.e., predicting a favorable market) or unfavorable (i.e., predicting an unfavorable market). Develop a decision tree for Jerry.
Question 2 Mike is a first year university student who is trying to understand his financial situation. Mike currently lives 1.5 miles away from campus. He works part time in a retail centre that pays him £800 per month. Mike saves £200 out of the part time job pay for his further education plan. a). As to the below Travel Expenses table published by the Students’ Union, 185 students were randomly selected to help understand the travel expenses and distance to campus. What’s the probability for Mike to spend over £10 on journeys to campus? Distance to Campus (miles) Amount spent, £ 0.1 to 0.25 0.26 to 1.0 Over 1.0 0 – 4.99 35 26 10 5.00 – 9.99 18 39 20 10.00+ 4 14 19 b). How much is the frequency for students living over 1 mile away from the campus? c). As to the category of Amount Spent, £, what is the modal group? d). Assuming Mike is saving the same amount per month in the next 3 years. How much does Mike get for his saving…
Question 1 What is the capacity of the system in the scenario below? Scenario: A large, high volume warehouse-style discount grocery & retail operation receives pallets of wholesale goods to stock their shelves. Each day the Shipping/Receiving (S/R) manager verifies & logs receipt of pallets which takes about 30 minutes (0.5 hours per pallet, hpp). The S/R manager then sends the received pallets to the staging area for pricing. It takes just about 75 minutes (1.25 hours) to price a pallet of goods; consequently, there are two “pricers”. The priced items are then place on the shelves throughout the warehouse by nine “stockers” at an average rate of about a pallet every 90 minutes (1.5 hours) per stocker. At the same time the stockers are placing items on shelves, an employee called a “shelf-spotter” rotates stock forward in the shelving to make room for the stockers which takes about 12 minutes (0.20 hours) per pallet-quantity of items. At the end of each day an analyst…
Question 1 A company manufactures two types of boxes, corrugated and ordinary cartons. The boxes undergo two major processes: cutting and pinning operations. The profits per unit are $6 and $4 respectively. Each corrugated box requires 2 minutes for cutting and each carton requires 3 minutes for cutting, whereas each corrugated box requires 2 minutes for pinning and each carton requires 1 minute for pinning. The available cutting time is 120 minutes and total pinning time is 60 minutes. Determine the optimum quantities of the two boxes to maximize the profits. a. Formulate a linear programming model that can be used to determine the quantities of the two boxes that should be produced in order to maximize total profit contribution.b. Graph the feasible region.c. Determine the coordinates of each extreme point.
Answer question 2
Question 2: Consider the network below with distances (shown in rectangles) in miles between the nodes (shown in circles). 1. Briefly describe if it is possible to develop an LP formulation of the above problem and how the the bigger instances of such problems can be solved. 2. Let us suppose you are working as an operations manager at a supermarket responsible for delivery of online orders of grocery items. Briefly describe how you will make use of the Shortest Route problem in the daily efficient delivery operations with given customer orders receiving times.
Question 4Consider a birth death model with birth rates in states n = 0, 1, . . . and death rates in states n = 1, 2, . . (a) Give the detailed balance conditions for the equilibrium probability of being in state n, for n = 0, 1, . . . and explain how they are derived. (b) Using the detailed balance conditions derive an expression and state any condition needed to ensure that the equilibrium distribution exists. (c) i Now consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of , the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distribution
Problem #3 A, B, C

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