Can someone walk me through this answer?

for Question 1 where does wiT come from and why does it =C to become 2C?

wjT + C = 24wp

Section V [21 points total] Suppose poor households have preferences over consumption (C) and leisure (T) given by u (C, L) = log (C) Hog (T), and they can work at wage wp = 5. Assume consumption costs one dollar, and they have 24 hours in a day to allocate to either leisure or working- 1. Solve for the household's optimal bundle of consumption and leisure. How much utility do they get? (7 points] MUC MUT MUT MUC -10- 16 -PHD C 24up 20 24w = C = 12wp Thus they consume 60 and get utility log (60) + log(12) ~: 6.5793 2. To try and help the poor, the government offers an income transfer of $20, but because picking up the check takes time, participants can only work 5 hours per day if they sign up for the program. (Continue to assume any time not spent working is leisure). Find their optimal bundle under the program. [7 points] With no restrictions on time the poor would choose, = 24wp + 20 2 = 70 T 24w + 20 201p = 14 But that violates the terms of the program, so instead they get as close to this allocation as they can and choose C+w19 = 24wp + 20 C = 50p + 20 = 45 = 19