(3) The Western Cape government has decided to develop four desalination plants to combat the negative...

  

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(3) The Western Cape government has decided to develop four desalination plants to combat the negative effects of climate change. A total of five contractors have submitted bids during the tender process. Based on the completion of previous, similar projects by the five contractors, government officials have calculated the expected cost (in R1 000 000's) shown in the following table. Plant 2 Plant 3 Plant 4. Plant 1 9 7 9 10 10 Contractor 1 Contractor 2 Contractor 3 Contractor 4 Contractor 5 14 17 18 12 15 19 20 21 18 21 15 19 18 19 16 In order to expedite the execution of this project, only one contractor is awarded the development of a desalination plant. Suppose the government only has R50 000 000 available and wants to determine a contractor-desalination plant assignment resulting in the smallest overall cost. Formulate the problem mathematically as an assignment problem. (Hint: The number of desalination plants is small than the number of contractors. A dummy desalination plant must therefore be inserted in order to transform the problem into a classical assignment problem.) Define your decision variables precisely and include short explanatory comments for each model constraint. Furthermore, use both the Hungarian method and an appropriate computer implementation (e.g. Microsoft Excel's Solver add-on or Python packages such as Scipy & PuLP) to determine an optimal assignment. If it is necessary to seek supplementary funds, how much money should the government seek? Finally, which of the five contractors will be unsuccessful? Please include a carefully commented print-out of your program embedded within your PDF submission. [36] (3) The Western Cape government has decided to develop four desalination plants to combat the negative effects of climate change. A total of five contractors have submitted bids during the tender process. Based on the completion of previous, similar projects by the five contractors, government officials have calculated the expected cost (in R1 000 000's) shown in the following table. Plant 2 Plant 3 Plant 4. Plant 1 9 7 9 10 10 Contractor 1 Contractor 2 Contractor 3 Contractor 4 Contractor 5 14 17 18 12 15 19 20 21 18 21 15 19 18 19 16 In order to expedite the execution of this project, only one contractor is awarded the development of a desalination plant. Suppose the government only has R50 000 000 available and wants to determine a contractor-desalination plant assignment resulting in the smallest overall cost. Formulate the problem mathematically as an assignment problem. (Hint: The number of desalination plants is small than the number of contractors. A dummy desalination plant must therefore be inserted in order to transform the problem into a classical assignment problem.) Define your decision variables precisely and include short explanatory comments for each model constraint. Furthermore, use both the Hungarian method and an appropriate computer implementation (e.g. Microsoft Excel's Solver add-on or Python packages such as Scipy & PuLP) to determine an optimal assignment. If it is necessary to seek supplementary funds, how much money should the government seek? Finally, which of the five contractors will be unsuccessful? Please include a carefully commented print-out of your program embedded within your PDF submission. [36]

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To formulate the problem as an assignment problem we need to create a matrix that represents the costs of assigning each contractor to each desalinati... View the full answer