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]