Question: 1. [35 marks] Consider the following linear programming problem. Maximise 10x, + 5x2 + x3 Subject to 2x, + x2 + xz 28 x; +

1. [35 marks] Consider the following linear

1. [35 marks] Consider the following linear programming problem. Maximise 10x, + 5x2 + x3 Subject to 2x, + x2 + xz 28 x; + 2 x, - xz = 12 5x, + 2 xz 510 xy, X2, X3 20 (a) Use the simplex method to solve the maximization problem. [20 marks] (b) is the optimal solution you obtained above unique? If unique, why? If not, unique, then what is (are) the alternative solutions(s)? [5 marks] (c) Which constraint(s) is (are) non-binding? [4 marks] (d) Find the dual price for the first, second and third constraints from the final simplex tableau you get. What are the interpretations of these dual prices? [6 marks]

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