The accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery. E 200 X3 D 150 X5 X4V 200 25 A X2 B 175 C (a) Set up a linear system whose solution provides the unknown flow rates. XI 25 X2 175 X3 Find A so that A = y where = 200 and y= 150 X5 200 X6 Form the system so that the first equation represents node A, the second equation node B, etc. Then take all the variable to one side such that all the constants are on one side and positive. From the equations form the required matrices and enter the appropriate values for A below. A = X₁ x6 Mi
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- A group of n tourists must cross a wide and deep river with no bridge in sight. They notice two 13-year-old boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold two boys or one tourist. How can the tourists get across the river and leave the boys in joint possession of the boat? How many times need the boat pass from shore to shore?As we all know, heuristic or approximation algorithms may not always provide the best solution to a problem, but they are very efficient in terms of polynomial time. (a) Propose an approximation method for the travelling salesman problem (TSP) and analyze the time complexity and limitations of the proposed approach. (2) Provide two examples of inputs for which the method in (a) produces the best and not-the best answers, respectively. (3) There should be between six and eight nodes in each network.The multiple connected zones of Hamilton are shown in a planar map, in the following Fig.1. Drawthe planar graph for the following map (in Fig. 1) of multiple connected zones. Find out the minimum numberof frequencies needs to be used using graph theory, so that different zones of the following planar map areassigned with different frequencies (i.e., each zone operates at one single frequency) in such a way that noadjacent zones (i.e., zones with common borders) use the same frequency? The frequencies available for useare 10 GHz, 20 GHz, 40 GHz, 60 GHz, 80 GHz, 100 GHz, 120 GHz, and 140 Hz. Show your detailed work. Fig. 1: Spectrum division of Hamilton
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