3. Aurelie has chosen to get out of the toy princess industry, and has started selling toy cars, instead. She produces toy cars using labor (L), and capital (K) according to the production function, Q = LiKi, The perunit price of labor is w, and the perunit price of capital is r. (a) Write down the cost-minimization problem and the associated Lagrangian. Com pute the rst-order conditions, and use them to show that cost minimization requires MRTSLK : %. (10 points) For the remainder of the question, assume w = r = 2. (b) Solve for the conditional factor demands. (15 points) (c) Solve for Aurelie's cost function, the average cost function, and the marginal cost func tion. (10 points)