I would like to confirm the answer all from (a) to (e).

2. A firm has a production function given by F(K, L) = K\"2 + L\"2 (a) Write down the firm's cost minimization problem (what are they trying to minimize? What is the constraint?) and the Lagrangian to solve the problem. (b) Find the firm's contingent demands for L and K as a function of Q, to and 12 using the Lagrangian. (c) Find the firm's total cost function (d) Find the firm's average cost function (e) Find the firm's marginal cost function