1. Optimization: From Dixit's excellent book \"Optimization in Economic Theory" (35 points) There is a fixed total Y = 1 of goods at the disposal of society. There are two con- sumers who envy each other. If consumer 1 gets Y1 and consumer 2 gets Y2, their utilities are u, = Y1 kit/22,- u; = Y2 Fri/12, where k is a positive constant. The allocation must satisfy the resource constraint: Y1 + Y; S 1'. You are the social planner who is trying to find the allocation that maximizes the utilitarian welfare function of U1 + U2. Setup the social planner 's optimization problem. (5 points) What are the optimal allocations when k = 1.7 (10 points) What are the optimal allocations when k = 2? (10 points) 9053'?\" Show that if Y :> 35, the resource constraint will be slack at the optimum. Inter- pret this result. (10 points)