A company manufactures two types of smart gadgets: Gadget X and Gadget Y. The company aims to maximize its profit while adhering to manufacturing, resource, and market constraints. The company has formulated the following Linear Programming (LP) model: Maximize Z = 500 X 400 Y subject to 50 X 25 Y 300 (manufacturing time constraint) 6 X 15 Y 60 (resource availability constraint) - X 2 Y 4 (production balance constraint) X, Y 0 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)