Solve please

The unisex single model of labor supply. Suppose the household utility function is given by: Where It) 220 is a constant. It is the subsistence level of consumption; where, consumption, c, must be at least as large as [psi] for the household to have any utility. The household has 1 unit of time, and can be divided into either working in the market at wage w or leisure, l. a. Solve the household's maximization problem. b. How does a rise in the wage rate, w, impact on time spent in the market and leisure? Represent it graphically. Lastly, explain how does Psi works? c. In 1900, a man worked 70 hours a week, with the wage rate in 1900 of 1. In 2000, it dropped to 42 hours per week, with the wage rate was 9 times larger. Is the unitary model capable of explaining these facts? Why