Solve the following linear program using the graphical method (graph sheet on next page). Identify the...

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Solve the following linear program using the graphical method (graph sheet on next page). Identify the decision variables. Compute the value of the decision variables and the objective function at optimality and indicate which statement best describes the solution. (10 points) Max Z = 9x+6y Subject to: 3x+2y≤ 30 -6x+3y ≤ 12 4x-2y ≤ 20 y≤7 x, y ≥0 (a) This linear program has a unique optimal solution (b) This linear program has alternate optima (c) This linear program is infeasible (d) This linear program is unbounded Suppose you are able to find a feasible solution to the dual of a linear program, and suppose that this dual feasible solution has a positive dual objective value. What can you say about the feasibility of the original linear program? (If you are unsure about your answer, write your thoughts down for partial credits.) (a) The original linear program is feasible. (b) The original linear program is infeasible. (c) It is not possible to say whether the original linear program is feasible or infeasi- ble based on this information. Solve the following linear program using the graphical method (graph sheet on next page). Identify the decision variables. Compute the value of the decision variables and the objective function at optimality and indicate which statement best describes the solution. (10 points) Max Z = 9x+6y Subject to: 3x+2y≤ 30 -6x+3y ≤ 12 4x-2y ≤ 20 y≤7 x, y ≥0 (a) This linear program has a unique optimal solution (b) This linear program has alternate optima (c) This linear program is infeasible (d) This linear program is unbounded Suppose you are able to find a feasible solution to the dual of a linear program, and suppose that this dual feasible solution has a positive dual objective value. What can you say about the feasibility of the original linear program? (If you are unsure about your answer, write your thoughts down for partial credits.) (a) The original linear program is feasible. (b) The original linear program is infeasible. (c) It is not possible to say whether the original linear program is feasible or infeasi- ble based on this information.