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Problem 2 ( 23 points) Solve the following linear programming problem graphically: Maximizesubjectto Z=500x1+400x2 10x1+20x25x1+10x24x12x2x1+2x2100501015x1,x20 a. Graph the constraints (make sure to label them clearly to indicate which line corresponds to which constraint) and identify the feasible region (Shade/darken the feasible region). Provide all necessary steps/calculations to justify your answers. ( 13 points) b. Draw the objective function, then determine the optimal solution(s) and the maximum value of the objective function. Provide all necessary steps/calculations to justify your answers. (7 points) c. What other method can you choose to find the optimal solution without drawing the objective function? Considering the structure of the feasible region, which method is better? Justify your answer. ( 3 points)