Please help me on this question

2. Consider a low-income single mother named Jane. Jane has 2,000 hours that she can allocate to work (H) or to leisure (L), so H+L=2,000. If she works, she receives an hourly wage of $10. Any income she earns from working, she spends on food (F), which has price $2. Jane's utility function is given by U(F,L) = 150*In(F)+100*In(L). The government runs a TANF program, which is defined by a benefit guarantee (BG) of $5,000 and a benefit reduction rate (BRR) of 50%. a. How many hours, H*, does she have to work to become ineligible for the program? b. Draw Jane's budget constraint on a graph with food units on the y axis and leisure units on the x axis. (Be careful: note that the price of food is $2, not $1!). c. Write down a piecewise function for Jane's effective wage. d. Assume that Jane works more than H* hours (your answer from part a) and therefore is ineligible for TANF. What bundle of food and leisure would she choose? What would her utility level be as a result? (Note that SU /8F = 150/FandoU/SL = 100/L). e. Assume that Jane works fewer than H* hours and therefore participates in TANF. be? What bundle of food and leisure would she choose? What would her utility level f. Compare the utility levels computed in parts (d) and (e). Would Jane choose to participate in TANF or not