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The Ministry of water resources has stated that like Punjab, Uttar Pradesh (UP) is mining its groundwater. While Punjab has approximately one year's worth of

The Ministry of water resources has stated that like Punjab, Uttar Pradesh (UP) is mining its groundwater. While Punjab has approximately one year's worth of water demand stored in the ground, UP only has 20 years. Hence, a new plan to regulate and manage the groundwater resources of UP is needed. The legislature and Governor have formulated and implemented a new plan to preserve the integrity and sustainability of the Commonwealth's groundwaters with the following objectives: i) to minimize the extraction of groundwater and ii) to minimize the overall cost. The cost is the combination of the cost of the actual extraction of groundwater and the opportunity cost (due to the use of other sources of water i.e., the benefit that could be derived from the best alternative water use). The multi-objective problem has been simplified as follows: J1 = min {(x1)2} J2 = min {x1+ x2} The following constraints are given: x1 (x2+ 1) 10 2x1 +x2 16 x1, x2 0 Problem Solving: Using Matlab, Excel, or any other programming software of choice: Determine the feasibility region; Determine the efficient decisions, i.e., define the Pareto Frontier, using the weight method and the constraint method. Extra 20 points: use both weight and constraint method to identify the Pareto Frontier.

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