Consider a production function that transforms a workerjs leisure into bread so that 5(5) 2 100 52 where l E [0, 10] denotes leisure and 5(5) is the amount of bread produced as a function of leisure. 1. Assuming free disposal, draw the production possibility set on the Cartesian plane with axes leisure and bread. Put leisure on the horizontal axis. (5 pts.) 2. Is the production possibility set convex? Explain your answer using either a formal denition of a convex set or an illustration on your drawing. (5 pts.) 3. Explain what your answer to part (2) (convex or not) implies about the returns to scale of this production process. (5 pts.) Now suppose that the worker may consume the bread produced with her labor (the comple ment of leisure). Her preferences over leisure and bread are monotonic, and she is indifferent between three allocations CU : (10,0), E : (0, 100), i : (6, 64). 4. On the Cartesian plane with axes leisure and bread (leisure on the horizontal axis), draw an indifference curve through the points 33, :E, 1%. Indicate on your drawing the allocations that are in the \"betterthan\" set dened by the indifference curve you drew. The allocations in the \"betterthan\" set do not have to be feasible. (10 pts.) 5. Now consider the set, call it Y, consisting of allocations in the \"betterthan\" set you drew. Is that set Y convex? Explain your answer using either a formal denition of a convex set or an illustration on your drawing. (10 pts.) 6. Explain what your answer to part (5) (convex or not) implies about whether the marginal utility the worker receives from additional consumption of leisure is increasing or decreasing in the level of leisure. (10 pts.)