NEED HELP ASAP PLEASE!!!

1. Let T = 24 be total available hours (note that T = 24. not T = 12), 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 C be consumption. Treat each part of this question as a separate and independent scenario. Assume that the utility function is u(L, C) = LC. (a) Suppose that the agent receives a lump-sum amount of B dollars if he works 8 hours or more, i.e., n 2 8. Find (L*, C*) 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. (1 point) (c) Suppose that the law forces the agent to work no less than 3 hours and no more than 8 hours, i.e., n E [3, 8]. Find (L*, C*) and illustrate graphically your solution. (1 point) (d) Suppose that the agent receives an amount B > 0 when he doesn't work, i.e., n = 0. Find (L*, C*) and illustrate graphically your solution. (1 point)