(a) Use the transportation simplex method to solve the above problem
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- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…Explain how to determine the number of variables and constraints that would be in a transportation problem simplyby knowing the number of sources and the number of destinations.
- Consider the transportation problem having the following data: c) write the algebraic formulation of this problem.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.Construct a linear programming problem including at least three decision variables and three constraints. Formulate this problem and solve it by using QM for Windows Linear Programming module. Report your solution results and explain your findings.
- Using the template provided. Formulate a linear programming model (identify and define decision variables, objective function and constraints) that can be used to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers Use Solver in Microsoft Excel to solve the model. Give the values of each decision variable and the objective function. Please show how you solved it.In a typical network model representation of the transportation problem, the nodes indicate a. roads b. rail lines c. geographic locations d. rivers For all routes with positive flows in an optimized transportation problem, the reduced cost will be: a. zero b. how much less shipping costs would have to be for shipments to occur along that route c. how much more shipping costs would have to be for shipments to occur along that route d. how much the capacity is along that shipping route The decision variables in transportation problems are: a. profits b. costs c. flows d. capacities Which of the following statements is a type of constraint that is often required in blending problems? a. Integer constraint b. Quality constraint c. Binary constraint d. None of these options When a workforce…The optimal solution to the original Grand Prix problem indicates that with a unit shipping cost of $132, the route from plant 3 to region 2 is evidently too expensive—no autos are shipped along this route. Use SolverTable to see how much this unit shipping cost would have to be reduced before some autos would be shipped along this route.
- Consider the following transportation problem (cost in rupees). Find the initial solution by using Vogel’sApproximation method and perform optimality test using MODI MethodIn 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.The Sunshine Rental Car Agency has six lots in Orlando,and it wants to have a certain number of cars available ateach lot at the beginning of each day for local rental. Theagency would like a model it could quickly solve atthe end of each day that would tell how to redistribute thecars among the six lots at the minimum total mileage.The distances between the six lots are as follows: