working and detailed explanation

4. (Sundaram Chapter 6, Exercise 12) A firm produces a single output y using three inputs X1, 12 and *3 in non-negative quantities, through the relationship y = g(x1, X2, 23) = 21(22+23). The unit price of y is py > 0, while that of the input x; is wi > 0 for i E {1, 2, 3}. (i) Describe the firm's profit-maximisation problem, and derive the equations that define the critical points of the Lagrangian L in this problem. (ii) Show that the Lagrangian & has multiple critical points for any choice of (Py, W1, W2, W3) E R4. (iii) Show that none of these critical points identifies a solution of the profit maximisation problem. Can you explain why this is the case