Suppose the production function is f($1, 12) = ] /3 2/ (a) Formulate the profit maximizing problem for this firm and find the as- sociated first-order conditions. (b) Find the demand functions for r, and r, and the profit-maximizing quantity of output.Suppose from now on that the production function is f ($1, 12) = 1 2. (c) Repeat your computations for the new production function: formulate the profit maximizing problem for this firm and find the demand func- tions for r, and r2 and the profit-maximizing quantity of output. (d) We have seen earlier in class that increasing transformations of utility functions give rise to equivalent utility functions. Use your answers to (a)-(c) to argue that the same is not true for production functions. Why not