Problem 1 [800] The following multiple objective linear program [MOLP] has been formulated by Tarrant Water Management District (TWMD) for its water supply and energy program seeking to maximize the benefits from water supply and hydropower production accruing from the reservoirs it operates. To do so, TWMD has identified two (2) objectives. Objective one (PowerGen) is to maximize hydropower production (MegaWatts) from its reservoirs through water diverted to reaction turbines (TWMD uses Francis turbines). Objective two (WaterUsers) is to maximize water supply measured by the number major water users (thousands) TWMD meets their weekly demands. Maximize Maximize WaterUsers = 50 X1 + 120 X2 PowerGen = 80 X1 + 50 X2 s. t. 3 X1 + 4 X2 s 68 2 X1 30 2 X2 2 2 X1 > 2 X1 + 2 X2 10 X1, X2 > 0 (a) [75] Plot the feasible region in Decision space. Label the feasible extreme points starting with the uppermost one as A and so on, clockwise, in alphabetical order. X2 is the ordinate (y-axis). (b) [125] Determine the solution that optimizes each Objective Function and plot the objective function through each optimal point. Identify these solutions on your graph. i. [50] Use LINDO to solve the LP model using 1 objective as a time (there will be 2 LINDO models). ii. [50] Discuss each solution stating the reason each solution makes sense. What are the implications of the results? 3600002 (1) (2) (3) (4) (5) (6) (7) (c) [100] On a separate sheet of graph paper, plot the feasible region in Objective space. Label the extreme points of this graph in such a way as to show the correspondence between the feasible extreme points in Decision space and those in the Objective space. PowerGen must be the ordinate (y-axis). (d) [100] Tabulate the values of the extreme points of the feasible region in Decision space and those in Objective space. (e) [50] Identify the non-inferior set in Decision space and Objective space (This is the trade-off curve in objective space) (f) [50] Is point the C dominated by point D in Objective space? Why? Please explain your reasoning FULLY