solve all with details explanation

2. Given the production function f (1,. x2 . x3) = xlmfnlxz. :13} , and factor prices w1 = w2 = w3 =1 (a) Calculate profit maximizing supply and demand functions, and the prot function. (13) Fix 3!. Calculate conditional demands of inputs and the cost function c(w,, w1, w3, y) (c) Solve the problem max py - :2th , w2 J\"? Y) 1 do you obtain the same production plan as in (b)? Explain your findings