For each of the following programs: (1) Sketch the feasible region of the program and the direction of the objective function. (2) Use you sketch to find an optimal solution to the program. State the optimal solution give the objective value for this solution. If an optimal solution does not exist, state why. (3) Transform the program into standard equation form. (4) List all basic feasible solutions of your standard equation form program. You should give the values for both the original decision variables and the slack variables in each of these basic feasible solutions. (a) maximise - 2x1 + x2 subject to X1 – x2 < 1, 2x1 – x2 > 1, 2.x1 + 2x2 > 4, X1, x2 >0

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