A sales director who lives in city A is required to fly to regional offices in cities B, C, D, and E. The weighted graph shows the one-way airtares between any two cities Use the Brute Force Method to find the optimal solution 14 220 Which Hamilton circuit is the optimal solution? How much will the sales director pay for airtare it he flies this route?
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- Suppose a salesperson is planning a sales trip that includes n cities. Each city is connected to some of the other cities by a road. To minimize travel time, the salesperson wants to determine the shortest route that starts at the salesperson’s home city, visits each of the cities once, and ends up at the home city. This problem of finding the shortest route is called the Travelling Salesperson Problem (TSP) and is a well-known problem that can be solved using Dynamic Programming. Research about the TSP problem and find an algorithm based on Dynamic Programming for that. Explain the approach, the algorithm, and its time complexity. Use an example to explain the way the algorithm operatesThere are 9 towns A, B, C, D, E, F, G, H, I. There are streets between them with distances shown below. Find shortest paths from A to C, A to D, A to E, and A to F. Specify the shortest paths and the shortest path lengths. You must use the Dijkstra’s algorithm table to solve this problem. Show all steps of your work. The streets and distances are AB 2, AG 4, AH 9, AF 6, BC 9, BG 8, CD 5, CG 2, DE 8, DG 3, EF 4, EH 7, EI 3, FH 2, GI 6, HI 5.In the graph in Figure 1, use Dijkstra's algorithm to find the shortest path from u to v. When choosing between two options of equal current distance, choose the first one alphabetically. U 5 7 2 b 3 2 1 1 1 d Figure 1: Apply Dijkstra from u to v 5 4 1
- A regional telephone company had 5.2 million subscribers. Each of their telephones is connected to a central office by a copper twisted pair. The average length of these twisted pairs is 3.5 km. How much is the copper in the local loops worth? Assume that the cross section of each strand is a circle 1.2 mm in diameter, the density of copper is 8.4 grams/cm3, and that copper sells for $15.00 per kilogram.Question: Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. The gossip problem asks for G(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. a). Find G(1), G(2), G(3), and G(4). b). Use mathematical induction to prove that G(n) 4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.] c). Prove that G(n)= 2n – 4 for n> 4.There are 5 towns A, B, C, D, E. There are one way streets between them with distances shown below as an adjaceny matrix. Find shortest paths from A to C, E to A, C to B, and E to C. Specify the shortest paths and the shortest path lengths. You must use the Floyd’s algorithm. Show all steps of your work. A B C D E A 0 2 9 5 6 B 1 0 3 4 2 C 6 9 0 1 5 D 2 4 1 0 2 E 8 3 5 1 0
- The diagram below shows roads connecting towns near to Rochdale. The numbers on each arc represent the time, in minutes, required to travel along each road. Peter is delivering books from his base at Rochdale to Stockport. Use Dijkstra's and Bellman-Ford's algorithm to find the minimum time for Peter's journey. Show every iteration for D and P. Which algorithm is more efficient in this example? Rochdale 15 10 Bury 25 8 14, Oldham 17 23 14 Trafford Manchester 17 20 Ashton 13 StockportYou are currently building an set of office network infrastructure. When connecting two computers, assume that the chance of a network outage drops by a factor of 10. That is, two computers connected to each other have a 10% chance of network failure, while three computers have a 1% chance. How would you determine how resilient your network is given a graph of all computers and their connections to one another? O Determine the k-regularity of the graph, use this value of k to calculate network resiliency. O Determine if there is a Hamiltonian path within your network, use the length of this path to calculate network resiliency. 4 Invert the graph, find the vertex with the smallest degree, and use this degree to calculate network resiliency. O Find a k-coloring such that k is minimized, us this k to calculate network resiliency.A city would like to know how many vehicles it could move through its streets in an emergency. The most likely situa evacuation starting at the school and ending at the park. The connections between these two locations, plus their cap direction, is shown below. C Oak Street 1" Street F School Park B Elm Jad Street Street E A Path Capacity Б C D 30 20 E F 25 25 30 25 20 (Round your answer to the nearest whole number.) Maximum Flow
- The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean $4.59 and a standard deviation of $0.10. Sixteen gas station from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16-gasoline station. Which of the following distribution to use? X ~ N (4.59,0.16/√10) XN (4.59,0.10) XN (4.59,0.16/10) WXWX WWWX wwxx XXWW ~ N (4.59,0.10/√16)A local café has a single cash register, with a single assistant to work it, and three serversworking to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds.Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.a. Calculate the capacity of the register and the servers. What is the bottleneck inthis system?b. Calculate the average utilizations of the register and the serversc. What is the probability a customer is delayed at the register?d. What is the expected time from a customer’s arrival to the order being passed on tothe servers (including any queueing time)?e. Estimate the probability that there is a delay between a customer placing his orderand a server beginning to work on the…The following below gives the gain of an antenna and efficiency. Use it to solve the following question G = 10'log10 ( K" (("DYA)?). Where, G is Gain in dB K is efficiency of antenna Dis antenna diameter(m) A = c/f,f=operating frequency c=3 x 10° m/s G/10 Efficiency = (AD(10) Let initial Antenna diameter = 2.4 meter, Antenna Gain (dBi) = 43, Antenna frequency = 6000 MHz Vary D from 2.4 to 5.6 with a change of 0.2. i. Plot a graph of K vrs D for D=2.4 to 5.6 with a change of 0.02 ii. Plot a graph of K vrs D for D=2.4 to 5.6 with a change of 0.01 iii. Write a c++ code to solve for i. iv. Write a c++ code to solve for ii.