How does linear equations can help to find a solution to the transportation, assignment and transshipment problems
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- PLEASE SHOW ALL FORMULA PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1…Find the optimal solution for the transportation problem having the cost and requirement table below. -Solve the following transportation models using Excel Solver.ii. The problem seeks to minimize total transportation cost. What will be the objective function in terms of x and y?
- 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.Suppose there is a transportation model with 4 factories and 6 warehouses. In order to develop an initial solution using the intuitive lowest cost method, do we have to add one or more dummy sources in the transportation matrix, and why?Four cargo ships must be used to transport goods from one port to four other ports (numbered 1, 2, 3, and 4). Any boat can be used to make any of the four trips. However, given some differences between ships and cargoes, the total cost of loading, transporting, and unloading goods from different combinations of ships and ports varies considerably. These costs are shown in the following table: The goal is to assign ships to ports in a one-to-one correspondence so that the total cost of the four shipments is minimized. a) Describe how this problem can be adapted to the general format of assignment problems. b) Obtain an optimal solution using Excel Solver step by step
- The more sources and destinations there are for a transportation problem, the smaller the percentage of all cells that will be used in the optimal solution. Explain.Illustrate through your own example degeneracy in transportation problems. Can the optimal solution still be reached when one encounters degeneracy in a transportation problem? Justify your answerDraw the network for this transportation problem. (Let xij represent the flow from node i to node j.) Min 2x13 + 4x14 + 6x15 + 8x23 + 11x24 + 9x25 s.t. x13 + x14 + x15 ≤ 500 x23 + x24 + x25 ≤ 400 x13 + x23 = 300 x14 + x24 = 300 x15 + x25 = 300 xij ≥ 0
- Oranges are grown, picked and then stored in warehouses in Tampa, Miami, and Fresno. Theses warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload (in hundreds of dollars), supply, and Because of an agreement between distributors, shipments are prohibited from Miami to Chicago: Draw a network of this problem. Formulate a linear program for this problem.Explain how balancing a Transportation Problem If Total Supply Is Less Than Total Demand in linear programming. Please give your exampleConsider the following network representation of a transportation problem: The supplies, demands, and transportation costs per unit are shown on the network. Whatis the optimal (cost minimizing) distribution plan?