What is a reservation wage?

Peggy is a single mother who currently does not work and has a two year-old child named Bud. Peggy’s concerned parents give her $30/day (non-labor income) to support her and Bud. Peggy has just interviewed for a job as a cashier at Kroger’s grocery store. They are willing to hire her at a wage of $8/hour. If Peggy takes the job, she will have to pay $20/day for childcare while she is at work. This question concerns Peggy’s decision on whether to take the job.
a) What is a reservation wage? Suppose that Peggy is unwilling to take the cashier’s job at the current offered wage of $8/hour. What does this imply about her reservation wage?
b) Suppose that Peggy can work at most 16 hours in a day and that if Peggy works even one hour she has to pay the $20 in childcare for Bud. Draw Peggy’s effective budget constraint and her indifference curve through her chosen point of not working which is consistent with what her preferences must be given that she chooses not to work at the current offered wage.
c) For the indifference curve you have drawn, show graphically Peggy’s reservation wage. Would she be more likely or less likely to take the job if her indifference curve was steeper than the one you have drawn? What does a steeper indifference curve imply about Peggy’s relative marginal utility of leisure? Suppose Kroger’s grocery store decides to offer free child care but does not change the wage they offered Peggy. Draw Peggy’s new budget constraint. Show graphically whether she is more or less likely to take the job now?