This is a optimalization problem.

I don't know 5-(e

. [40 points total] We want to find the global maximum of W (c1.C2, 1/1, 1/2) = Inc - 3 (un) + In cz (u2)? subject to C1 + c2 Sy1+U2. (1) In ci - 2 (1)2 2 In cz - 3 (uz)2 (2) Assuming that Ci, C2, y1, 12 > 0, answer the following questions. (a) [5 points] Set up the Lagrangian function of this problem, with A and / multipliers associated with (1) and (2), respectively. (b) [10 points] Write down all first-order conditions. (c) [5 points] Prove that the constraint (1) is binding, or equivalently, A > 0 at critical points. (d) [10 points] Show that the constraint (2) is also binding, or equivalently. u > 0 at critical points. (e) [10 points] Prove that the following conditions hold at the critical points. (i) = = V1 (ii) - > 12 (jii) 1 > ca