Q2: Consider the minimisation of the following function of two variables: f(x1, x2)=-In(1+x₁) = x₂. Subject to the linear constraints: 2x1 + x₂ ≤3; 21, x₂ ≥ 0. (a) Prove that

this is a convex minimisation problem. (b) Write down the Karush-Kuhn-Tucker conditions for this problem. (c) Find all solutions of the above KKT conditions. (d) Are the solutions you found a local or a global minimum (maximum)? Justify your answer. [15 marks]