Consider the optimisation problem: 

Maximize u(x_{1 ,} x₂)

subject toM= p₁x₁ + p₂x₂

where M, p₁ and p₂ are positive constants. Write down the Lagrangian for this problem and explain why you need to assume that an interior solution exists before using the Lagrangian method to solve the problem.  (100 words) (5 Marks)