East Coast Trucking provides service from Boston to Miami using regional offices located in Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savannah, Jacksonville, Tampa, and Miami. The number ofmiles between each of the regional offices and the numbers associated with each city are provided in the following table.BostonNew YorkPhiladelphiaBaltimoreWashingtonRichmondRaleighFlorenceSavannahJacksonvilleTampaMiamiNew York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami15652345ஈNOGE78911211320109424213104459248139353542451411067135023932892541488846735644604253191711,0568457366325974913431721,1969858767727376314833121401,399 1,6691,1881,079975 1,245834940 1,2106865151,4583431,3492031,104956785613473270The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located, such that each regional office is within 400 miles of at least one service facility. For instance, if a service facility isconstructed in Richmond, it can provide service to regional offices located in New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, and Florence. Management would like to determine the minimum number of service facilitiesneeded and where they should be located. (a) Formulate an integer linear program that can be used to determine the minimum number of service facilities needed and their location. (Let x; be the 0-1 variable, which is 1 if a service facility is constructed in city i, and 0otherwise.)Mins.t.BostonNew YorkPhiladelphiaBaltimoreWashingtonRichmondRaleighFlorenceSavannahJacksonvilleTampaMiamiX11 X2 X3 X4 X5, X61X71 X8 X9 X10 X11 X12 = 0, 1

A linear program model is a mathematical model with a linear objective function a set of linear…

Answered: ormulate an integer linear program that…

Practical Management Science

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Publisher:WINSTON, Wayne L.

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ElectroMart 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 and solve a model to find the best location, assuming that straight-line distances can be used between the locations The best location for the warehouse is at X....... and Y......... (Round to two decimal places as needed.)
East Coast Trucking provides service from Boston to Miami using regional offices located in Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savannah, Jacksonville, Tampa, and Miami. The number of miles between each of the regional offices and the numbers associated with each city are provided in the following table. New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami 4 2 3 4 5 6 8 La 1 1 1 211 320 109 424 213 104 459 248 139 35 565 354 245 141 106 713 502 393 289 254 148 884 673 564 460 425 319 171 1,056 845 736 632 597 491 343 172 1,196 985 876 772 737 631 483 312 140 1,399 1,669 1,188 1,458 1,079 975 1,245 940 834 686 515 343 1,349 203 1,210 1,104 956 785 613 473 270 The company's expansion plans involve constructing service facilities in some of the cities where a regional office is…
Facility Location. A paper products manufacturer has enough capital to build and manage some additional manufacturing plants in the United States in order to meet increased demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is considering building in Denver, CO; Seattle, WA; and St. Louis, MO. Max Operating Capacity 400 tons/day 700 tons/day Denver Seattle $10/ton $17/tor $5/ton $11/ton.... $18/ton.... $28/ton Los Angeles Topeka New York City Figure 1: Graphical representation of the given data = • The cost fi of building plants in these cities is fi $10,000,000 in Seattle. Unmet Demand 300 tons/day 100 tons/day 500 tons/day • Due to geographic constraints, plants in Denver and Seattle would have a maximum operating capacity kį of 400 tons/day and 700 tons/day respectively. $5,000,000 in Denver and f2 = • The cost cij per ton of transporting paper from city i to city j is outlined in Figure 1. • The unmet demand d, for Los Angeles, Topeka, and New…
A car company is planning the introduction of a new electric car. There are two options for production. One is to produce the electric car at the company’s existing plant in Illinois, sharing production with its other products that are currently being produced there. If the sales of the electric car are moderate, this will work out well as there is significant capacity to produce all of the products there. However, if sales of the electric car are strong, this option would necessitate Adding a 3rd shift, which would lead to significantly higher costs. Another option is to build a new plant in Ohio. The new plant would have sufficient capacity to meet whatever level of demand for the new car. However, if sales of the new car not strong, the plant would be underutilized and less efficient. Since this is a new product, sales are hard to predict. The forecast indicates there is a 60% chance of strong sales (annual sales of 100,000), and 40% chance of moderate sales (annual sales of…
4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2
A scientist solves a nonhomogencous System of 10 linear equations in 12 unknowns and finds that three of the unknowns are free variables. Can the scientist be certain that, if the right sides of the equations are changed, the new homogencous system will have a solution ? To get the answer for above question, answer the followings (a) What is the order of the coefficient matrix? (b) ColA is a subspace of the vector space (c) What is dim Nul A ? (d) Write down the rank theorem. (e) What is rank A ? (f) What is dimCoIA ? (g) What is the conclusion for scientist's problem.
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Minimize Z= x1+2x2-3x3-2x4 subject to: x1+2x2-3x3+x4=4 x1+2x2+x3+2x4=4 x1, x2, x3,x4 are equal or greater then zero
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Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny plans to test this hypothesis using a random sample of 81 families from each suburb. His null hypothesis is:

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ormulate an integer linear program that can be used to determine the minimum number of service facilities needed and their location (let x. be the 0-1 variable which is 1 if a service facility is constructed in city and 0