Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: Locations A B DCDE с F Areas 1,4,7 1,3,5,7 1,2,5 2,5,6 3,4,7 4,6 Areas 2 and 6 must be covered by at least 2 locations. The rest of the areas must be covered by at least 1 location. What is the minimum number of locations?
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- . You are managing a badminton tournament and need a game official for each of the four games. All the games occur at the same time in four different departments. The departments are Education, Accountancy, Nursing and IT. The four game officials live in different parts of Abra and will need to travel to the games and submit a travel expense according to the table below. The assignment is one official to one game location. Formulate this assignment question as an LP question to minimize cost to send the officials to their games. Game Locations Official Education Accountancy Nursing IT 1 60 155 190 215 2 75 200 120 105 3 110 180 130 165 4 55 122 110 70A truck driver has to deliver a load of lumber to oneof two construction sites, which are, respectively, 27 and 33 miles from the lumberyard, but he has misplaced theorder telling him where the load of lumber should go. The two construction sites are 12 miles apart, and, to compli-cate matters, the telephone at the lumberyard is out of order. Where should he go first if he wants to minimizethe distance he can expect to drive and he feels that(a) the odds are 5 to 1 that the lumber should go to theconstruction site that is 33 miles from the lumberyard;(b) the odds are 2 to 1 that the lumber should go to theconstruction site that is 33 miles from the lumberyard;(c) the odds are 3 to 1 that the lumber should go to theconstruction site that is 33 miles9-43. Northwest University is in the process of complet-ing a computer bus network that will connect com-puter facilities throughout the university. The prime objective is to string a main cable from one endof the campus to the other (nodes 1–25) throughunderground conduits. These conduits are shownin the network below; the distance between them isin hundreds of feet. Fortunately, these undergroundconduits have remaining capacity through which thebus cable can be placed.(a) Given the network for this problem, how long (inhundreds of feet) is the shortest route from node1 to node 25?(b) In addition to the computer bus network, a newphone system is also being planned. The phonesystem would use the same underground conduits. If the phone system were installed, the follow-ing paths along the conduit would be at capacity and would not be available for the computer busnetwork: 6–11, 7–12, and 17–20. What changes(if any) would you have to make to the pathused for the computer bus if the phone…
- Design a spreadsheet to compute the total rectilinear distance from a set of up to10 existing locations to any other location. Assume that existing locations areplaced in Columns A and B and the new location in cells D1 and E1. Initializecolumn A with the value of cell D1 and column B with the value of cell E1, so thatthe total distance will be computed correctly when there are fewer than10 locations.a. Suppose that existing facilities are located at (0, 0), (5, 15), (110, 120), (35, 25),(80, 10), (75, 20), (8, 38), (50, 65), (22, 95), and (44, 70), and the new facility is tobe located at (50, 50). Determine the total rectilinear distance of the new facilityto the existing facilities.b. Suppose the new facility in part (a) can be located only at x =0, 5, 10, . . . , 100and y = 0, 10, 20, . . . , 100. By systematically varying the x and y coordinates,find the optimal location of the new facilityA new stadium complex is being planned for Denver, and the Denver traffic engineer is attempting to determine whether the city streets between the stadium complex and the interstate highway can accommodate the expected flow of 21,000 cars after each game. The various traffic arteries between the stadium (node 1) and the interstate (node 8) are shown in the following 1 10 8 7 0 1 LO 5 0 N 3 3 4 CO 6 6 LO 5 4 5 0 0 0 2 LO 6 26 2 7 8 4 9 0 0 8 The flow capacities on each street are determined by the number of available lanes, the use of traffic police and lights, and whether any lanes can be opened or closed in either direction. The flow capacities are given in thousands of cars. Determine the maximum traffic flow the streets can accommodate and the amount of traffic along each street. Will the streets be able to handle the expected flow after a game? Hint: I would use LP to solve it.By Monday April 16th the following towns will need the numbers of coal cars listed: coal valley 30 Coaltown 45 Coal Junction 25 Coalsburg 20 Using a railway city to city distance chart, the dispatcher constructs a mileage table on this page. Minimizing total miles over which cars are moved to new locations, compute the best shipment of coal cars.
- A health Centre will be built to serve 7 communities. The geographical location of the communities and their population is shown in the table below. Communities A, X =2.5 (km), Y=4.5(km), Population( 000's)=2 Communities B, X =2.5 (km), Y=2.5(km), Population( 000's)=5 Communities C, X =5.5 (km), Y=4.5(km), Population( 000's)=10 Communities D, X =5 (km), Y=2(km), Population( 000's)=7 Communities E, X =8 (km), Y=5(km), Population( 000's)=10 Communities F, X =7 (km), Y=2(km), Population( 000's)=20 Communities G, X =9 (km), Y=2.5(km), Population( 000's)=14 There is a possibility of building the Centre in two communities, community C and F. Based on the Demand-Distance criterion what is your recommendation for the site of the Centre. The distances to be measured based on Rectilinear method. Based on…Jk.335. Propiem 14-8 Rent'R Cars is a multisite car rental company in the city. It is trying out a new "return the car to the location most convenient for you" policy to improve customer service. But this means that the company has to constantly move cars around the city to maintain required levels of vehicle availability. The supply and demand for economy cars, and the total cost of moving these vehicles between sites, are shown below. From To A B C Demand D $9 9 5 50 From/To $8 Candidate solution A B C Total shipped Cost A - B C Total costs 8 3 60 $6 8 3 25 $5 D 0 10 a. Find the solution that minimizes moving costs using Microsoft Excel. (Leave no cells blank - be certain to enter "0" wherever required.) Supply 50 40 75 30 165 165 E F G Supply $Show your step-by-step process using the SPECIAL PURPOSE LINEAR PROGRAMMING: ASSIGNMENT METHOD to solve this problem. Four Engineers are to work on 4 projects of Dora Company. The problem is to decide which engineer should be assigned to which project. Each engineer charges different fees on each project, due to distances of the projects and the complexity of the work. The cost of assigning particular engineers to particular projects are as stated below. The objective is to find the lease cost of assignment. Engineer 1 to Projects A, B, C, D = $11k, $8k, $10k, $7k respectively.Engineer 2 to Projects A, B, C, D = $6k, $5k, $3k, $8k respectively.Engineer 3 to Projects A, B, C, D = $4k, $8k, $10k, $9k respectively.Engineer 4 to Projects A, B, C, D = $11k, $10k, $5k, $7k respectively.
- Sarah has a startup business that makes two distinct bird feeders that she has designed. Sarah is planning on operating a small factory to build the bird feeders. She is looking at two possible locations, A and B. If she chooses location A, the lease on the building will be higher than location B, thus leading to higher fixed costs than what she would have with location B. However, if she makes more than 20,000 units, both locations will likely have to be expanded, both the physical buildings and the manufacturing equipment. Variable costs to produce each unit will vary by location as well as by product. For example, the first design will have variable costs of $10 and $15 in locations A and B respectively, while the second bird feeder design will have variable costs of $20 and $25 respectively depending on location. However, she thinks that variable costs will decrease if she sells more than 5,000 units, as she will receive discounts from her suppliers at that point. She is unsure of…Please I want to solve the point 1&2J 2 An electronics store wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given in the accompanying table. Develop a model to find the best location, assuming that straight-line distances can be used between the locations. Experiment with the model by testing each of the possible best solutions, included, to find the best location. Click here to view the data for the store locations and annual numbers of truckloads. Click here to view some possible best solutions. The best location is at____. (Type an ordered pair. Round each coordinate to the nearest integer as needed.)