1. (a) Solve the following linear programming problem by using the Simplex Method. Provide all the details and explanations. maximise 2 = 2.01 +502 + 3x3 subject to: 21 +2r2 0, 22 > 0, 13 > 0 Explicitly provide the optimal solution for the problem and the corresponding objective function value. [ 7 marks (b) Write the Dual problem for the problem in part (a). [3 marks (C) Write the Dual problem from part (b) in standard form, with non-negative right- hand side constants in the constraints. [2 marks (a) Suppose you need to find a feasible basic solution for the problem in part (e) by using the Two-Phase Method. Write the problem you would have to solve in the first phase of the Two-Phase Method. (Do not solve the problem.) [3 marks ] (e) Provide the solution of the Dual problem in part (b) by analysing the solution of the problem in part (a). [2 marks] (f) A business executive has the option of investing money in two plans. Plan A guarantees that each pound invested will earn 70 pence in one year, and plan B guarantees that each pound invested will earn 2.00 in two years. Plan A al- lows yearly investments, while in plan B, only investments for periods that are multiples of two years are allowed. How should the executive invest 100,000 to maximise the earnings at the end of three years? Assume all the intermediate earnings are re-invested. Formulate this problem as a linear programming prob- lem. (Do not solve the problem.) (8 marks