|×23X22X13X21 +X11X12 +Mins.t.X12X13X22X23+X11X21X21X22X11X23X12X13X11 X12' X13 X21• X22' X23 2 0(b) Solve the linear program to determine the optimal solution.CostAmountJefferson City-Des MoinesJefferson City-Kansas CityJefferson City-St. LouisOmaha-Des MoinesOmaha-Kansas CityOmaha-St. LouisTotalVIVII|||++ Consider the following network representation of a transportation problem.25Des Moines14Jefferson40City8Kansas15City81125Omaha2425St. LouisSuppliesDemandsThe supplies, demands, and transportation costs per unit are shown on the network.(a) Develop a linear programming model for this problem; be sure to define the variables in your model.

Suppose the no. of products transported from Jefferson City to Des Moines be x11 and so on. We take…

Answered: Consider the following network…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 72P

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Solve the following problems using Excel Solver or R Studio. A company produces cars in Atlanta, Boston, Chicago, and Los Angeles. The cars are then shipped to warehouses in Memphis,Milwaukee, New York City, Denver, and San Francisco. The number of cars available at each plant is given in Table 1. Eachwarehouse needs to have available the number of cars given in Table 2. The distance (in miles) between the cities is given inTable 3. Assuming that the cost (in dollars) of shipping a car equals the distance between two cities, determine an optimalshipping schedule.
A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.
Jefferson Distributing is analyzing distribution networks with either 4, 5, 6 or 7 warehouses to serve 200 major customers in Europe. Relevant costs include transportation cost from the warehouses to customers, fixed facility costs, and inventory costs in the warehouses. The table below shows the annual transportation cost produced by a facility location software tool for locating 4, 5, 6 or 7 warehouses for this company. Suppose that annual inventory cost for the network can be modeled as $800,000 times the square root of the number of warehouses. Thus, if the network has 4 warehouses, then the annual inventory cost would be $800,000 x √4= $1,600,000. Number of Warehouses Transportation Cost 4 8,000,000 5 6,500,000 6 5,000,000 7 4,400,000 a) If the annual fixed cost per warehouse is $1,000,000, how many warehouses should there be to minimize the total (transportation + warehouse + inventory) cost? b) Now suppose the…
A company has three manufacturing plants (in Atlanta,Tulsa, and Springfi eld) that produce a product that is then shipped to one of four distribution centers. Th e three plants can produce13, 18, and 12 truckloads of product each week, respectively. Eachdistribution center needs 10 truckloads of product each week. Th eshipping costs per truckload between the plants and distributioncenters are given in the table. Th e company needs to determinehow much to ship from each plant to each distribution center andwould like to minimize total shipping costs (a) Formulate an LP to minimize the total shipping costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution
In a 3 x 3 transportation problem, let xij be the amount shipped from source i to destination j and let cij be the corresponding transportation cost per unit. The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units, respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given us u1 = -2, u2 = 3, u3 = 5, v1 = 2, v2 = 5, and v3 = 10. a) Find the associated optimal cost. b) Determine the smallest value of cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.
A company supplies goods to three customers, who eachrequire 30 units. The company has two warehouses.Warehouse 1 has 40 units available, and warehouse 2 has 30units available. The costs of shipping 1 unit from warehouseto customer are shown in Table 7. There is a penalty for eachunmet customer unit of demand: With customer 1, a penaltycost of $90 is incurred; with customer 2, $80; and withcustomer 3, $110. Formulate a balanced transportationproblem to minimize the sum of shortage and shipping costs.
The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M. Which type of network optimization problem is used to solve this problem? Multiple Choice: Minimum Flow Problem Average-Cost Flow problem Maximum Flow Problem Shortest Path Problem Maximum-Cost Flow problem
General Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed in the file P05_54.xlsx, where a blank means that a shipment is not allowed. Los Angeles can produce up to 1600 cars, and Detroit can produce up to 3200 cars. Houston must receive 1800 cars, and Tampa must receive 2900 cars.a. Determine how to minimize the cost of meeting demands in Houston and Tampa.b. Modify the answer to part a if no shipments through Atlanta are allowed.
A company has four warehouses and six stores. The warehouses altogether have a surplus of 22 units of a given commodity, divided among them as follows: Warehouses 1 2 3 4 Surplus 5 6 2 9 The six stores altogether need 22 units of the commodity. Individual requirements at b stores 1,2,3,4,5 and 6 are 4,4,6,2,4 and 2 units respectively. Cost of shipping one unit of commodity from warehouse i to store j in $ dollars is given in the matrix below. Stores Warehouses 1 2 3 4 5 6 1 9 12 9 6 9 10 2 7 3 7 7 5 5 3 6 5 9 11 3 11 4 6 8 11 2 2 10 Required Formulate the mathematical model for the problem How should the products be shipped from the warehouses to the stores so that the transportation cost is minimum?
A refinery manufactures two grades of jet fuel, Fl and F2, by blending four types of gasoline, A. B, C, and D. Fuel Fl uses gasolines A. B. C, and D in the ratio 1:1:2:4, and fucl F2 uses the ratio 2:2:1:3. The supply limits for A, B.C, and D are 1000, 1200, 900, and 1500 bbl/day, respectively. The costs per bbl for gasolines A, B, C, and D are $120, $90, $100, and $150, respectively. Fucls Fl and F2 sell for $200 and $250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bbl/day, respectively. Develop an LP model to determine the optimal production mix for F1 and F2, and find the solution using Solver
A refinery manufactures two grades of jet fuel, Fl and F2, by blending four types of gasoline, A. B, C, and D. Fuel Fl uses gasolines A. B. C, and D in the ratio 1:1:2:4, and fucl F2 uses the ratio 2:2:1:3. The supply limits for A, B.C, and D are 1000, 1200, 900, and 1500 bbl/day, respectively. The costs per bbl for gasolines A, B, C, and D are $120, $90, $100, and $150, respectively. Fucls Fl and F2 sell for $200 and $250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bbl/day, respectively. Develop an LP model to determine the optimal production mix for F1 and F2,
Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________

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