3. Dwight is an employee in Dunder Mifflin. Beside working as a salesman, he enjoys spend- ing time in his beets farm as leisure. He has a utility function of the following: (70%) U(L, X) = min{5L, 3X}, where L is the time spent in beets farm and X is his consump- tion. If he works, he receives a real wage w. His endowment of time is T. And the price of goods, p, is also normalized to 1. (a) Consider the case where T = 100, w = 0.5, please write down and draw the budget constraint, denote it with BC, with L on the x-axis and X on the y-axis, and show the slope and intersections. %3D (b) Please solve for Dwight's optimal labor supply and optimal consumption. (c) Draw the solution {L*, X*} in the graph and denote it as eo, and an indifference curve IC, that provides the optimal utility level. (d) Now, Dwight realizes that he is eligible for a social benefit program that provides monetary benefit payment to beet farmers of $20 per period. Please write down the new budget constraint. (e) Please draw the new budget constraint, and denote it as BC1 (f) Please solve for the new optimal labor supply. (g) Draw the new solution {L, X;} in the graph and denote it as e1, and a new indiffer- ence curve IC that provides the new optimal utility level. (h) Please compare eo and ej. Explain why there is a difference or no difference.