Suppose that an employment insurance program requires a minimum of 14 weeks of working to be eligible for the unemployment benefits. The benefits pay 60% of weekly earning with a maximum of 30 weeks of unemployment periods. Assuming a weekly earning of $400 for a person, answer the following.

a.   Derive mathematical equations for income-leisure constraints for this individual.
b.   If an individual works 25 weeks only in a year, what is his gross income including earning and EI benefit?
c.   Discuss how this EI program improves the worker’s welfare. Clearly justify your answer based on graphs and computations.