{"id":4202,"date":"2021-10-29T10:19:39","date_gmt":"2021-10-29T10:19:39","guid":{"rendered":"https:\/\/assignmenttask.com\/answers\/?p=4202"},"modified":"2022-10-13T08:06:00","modified_gmt":"2022-10-13T08:06:00","slug":"mat2200-operations-research-1-assignment-4-answers","status":"publish","type":"post","link":"https:\/\/assignmenttask.com\/answers\/mat2200-operations-research-1-assignment-4-answers\/","title":{"rendered":"MAT2200 – Operations Research 1 Assignment 4 Answers"},"content":{"rendered":"

Get Assessment Solutions on MAT2200 – Operations Research 1 Assignment 4 – Semester 2<\/b><\/h2>\n

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Are You Searching for MAT2200 – Operations Research 1 Assignment 4 Answers? Get quick & easy operations research management assignment writing services<\/strong><\/a> by statistics experts @ Assignment Task Australia<\/strong><\/a>. 24×7 live tutor’s assistance. AssignmentTask.com is an online assignment help<\/strong><\/a> provider working in 24*7 environments employing more than 1000+ MBA\/PhD experts worldwide. Connect to our website and chat with our representatives any time.<\/p><\/blockquote>\n

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QUESTION \u00a01\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (20 marks)<\/strong><\/p>\n

Use the branch and bound method to solve the following Integer Programming problem:<\/p>\n

max z <\/em>= 2.<\/em>7x<\/em>1<\/sub> + 3.<\/em>9x<\/em>2<\/sub><\/p>\n

s.t.<\/p>\n

7x<\/em>1<\/sub> + 14x<\/em>2<\/sub> \u2264 <\/em>385<\/p>\n

5x<\/em>1<\/sub> + 14x<\/em>2<\/sub> \u2264 <\/em>338<\/p>\n

12x<\/em>1<\/sub> + 16x<\/em>2<\/sub> \u2264 <\/em>536<\/p>\n

x<\/em>1<\/sub>, x<\/em>2<\/sub> \u2265 <\/em>0 and are integers<\/p>\n

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QUESTION 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (30 marks)<\/strong><\/p>\n

Water from a proposed desalination plant is to be pumped through an existing network of pipes leading from the plant to a storage dam.\u00a0 The map in Figure 1<\/a> below represents the network of pipes where the nodes (2 \u2013 13) represent pumping stations and node (1) is the desalination plant and node (14) is the storage dam. The numbers on the arcs denote the maximum flow for each pipe in Megalitres per day. Moreover, flow in each pipe is restricted to one way but can be in either direction (see Figure 1 below).<\/p>\n

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Figure 1: Map of water pipeline network showing maximum flow restriction in each pipeline section.<\/p>\n

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a).\u00a0<\/strong> What is the maximum volume of water (in Megalitres) that can be pumped per day from the desalination plant to the storage dam? (15 marks)<\/strong><\/p>\n

b).<\/strong>\u00a0 Indicate clearly on a diagram the direction in which the water should be pumped in the network in order to maximize the volume of water pumped per (5 marks)<\/strong><\/p>\n

c).<\/strong>\u00a0 To satisfy the manufacturers specifications each pumping station must be connected to a network of higher quality pipes. The costs for upgrading each section of pipeline to the higher quality pipeline (in millions of dollars) are shown in Figure 2. The local council proposes to only initially upgrade some of the pipes so that the plant, dam and each pumping station, (1) through (14), is linked to every other location by sections consisting of only upgraded<\/p>\n

Which pipes should be upgraded if costs are to be minimized?\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (10 marks)<\/strong><\/p>\n

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Figure 2: Map of water pipeline network showing the cost of upgrading each section.<\/p>\n

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QUESTION \u00a03\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong> (30 marks)<\/strong><\/p>\n

A manager of theme park needs to check the paths between the park\u2019s attractions are clean and tidy before opening for the day. To do this the manager will choose a route such that she travels along each path once and once only <\/strong>to see and check if it is suitably clean. She does not mind if she has to pass through an attraction more than once as long she only travels along each path once and that the route begins and ends at the main gate located at L.<\/p>\n

Figure 3 shows the main areas of the theme park with the main gate designated as L and the attractions denoted by A, B, C, . . . , K, M. The paths between each of the attractions and with the main gate are denoted as a, b, c . . . w.<\/p>\n

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Figure 3: \u00a0A map of the theme park with the gate L and attractions at A, B, C,. . . , K, M.<\/p>\n

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