6. (4 points) Consider the production function f (x1, X2) = 2122 a where a E (0, 1). (a) Set up the cost minimization problem to produce a given output q 2 0 when input prices are w1 > 0 and w2 > 0. (0.5 points) (b) Find the optimality condition. (1 point) (c) Find the toal cost function. (1 point) (d) Short-Run. Suppose that input 1 is fixed at x1 = 1. i. Set up the short-run cost minimization problem. (0.5 points) ii. Find the short-run cost function. (1 point)