Given Adam's utility function as U = In(C) + In(1) where C and I represent Bananas and leisure respectively. The wage rate is $5 per hour and the price of bananas is $1.

(a) Calculate how many hours per day (24 hours). Adam should work to maximize his utility.

(b) Now, suppose Adam wins a lottery that gives him $100. calculate how many hours per day Adam should work to maximize his utility