Question 1 for economics mathematics

1. A perfectly competitive firm minimises cost subject to achieving a target level of output, with Lagrangian: L 2 WI. + 'rK + M6 L0-5K0-5) Derive the F.0.C.s for a minimum, take the total differentiais of each and place them in linear algebra form. Use Cramer's rule to derive an expression for (112. Which of the following statements is correct? (i) The denominator in Cramer's rule is the bordered Hessian for the problem, which satisfies the minimisation problem's 5.0.C. and hence the denominator has negative signl (ii) 6L 0 (iv) All of the above are correct (v) None of the above are correct