3. (8 points) Recall the consumption-leisure problem from homework 1. Be careful, I made a few modications in terms of values... That is, let T = 24 be total available hours, L be hours of leisure, and n be hours of work. Let w > 0 be the hourly wage and p > 0 be the price of the consumption good. Finally, let G be consumption.Assume that the utility function is u(0, L) = C =o< L. (a) Suppose that the agent receives a lump-sum amount of B dollars if he works more than 8 hours. Find (L*, 0*) and illustrate graphically your solution. (2 points) (b) Suppose that if the agent decides to work beyond regular hours (say 8 hours), then he is given an additional 7' dollars for every hour (beyond 8 hours). Find (L*, C\") and illustrate graphically your solution. (2 points) (c) Suppose that the law forces the agent to work no less than 3 hours and no more than 8 hours. Find (L*, 0*) and illustrate graphically your solution. (2 points) (d) Suppose that the agent receives an amount B > 0 only if the agent is inactive, i.e., n = 0. Find (L*, 0*) and illustrate graphically your solution. (2 points)