please help me solve this

Suppose households preferences are described by the utility function U(C, 1) = 31 1/2 + C, where C stands for consumption of market goods / stands for leisure. The total number of hours available to the representative consumer is 1, and the market real wage is w. Output is produced using the production function Y = (N") /2. For simplicity, let us assume hat there is no government, that is G =0. The firm distributes a profit a to the consumer. 1. Solve the consumer's problem and find the optimal values of (", /*, and then deduce N. [04 points] 2. Solve the firm's problem and derive N*. [02 points] 3. Compute the competitive equilibrium wage rate (w*), and deduce employment (N*), and the aggregate output (Y*) in this economy. [04 points]