3. (29 points total) Consider minimizing costs, wL+rk when LKP > Q and (w,r,Q) = (2, 12,3) and L > 0, K > 0. (a) (2 points) Set up the Kuhn-Tucker objective function for this prob- lem. (b) (6 points) Find all the first order conditions. I do not require you to solve this problem. The solution is (L,K) = (3,1), below you may need to find the multiplier(s) of the con- straint(s) yourself. (c) (2 points) Let (w,r,Q) be the cost function, when (w,r,Q) (2, 12,3) finde using the envelope theorem. (d) (6 points) Prove the result you just stated by proving the envelope theorem for this case. 3. (29 points total) Consider minimizing costs, wL+rk when LKP > Q and (w,r,Q) = (2, 12,3) and L > 0, K > 0. (a) (2 points) Set up the Kuhn-Tucker objective function for this prob- lem. (b) (6 points) Find all the first order conditions. I do not require you to solve this problem. The solution is (L,K) = (3,1), below you may need to find the multiplier(s) of the con- straint(s) yourself. (c) (2 points) Let (w,r,Q) be the cost function, when (w,r,Q) (2, 12,3) finde using the envelope theorem. (d) (6 points) Prove the result you just stated by proving the envelope theorem for this case