3. (a) Last year, a welfare-eligible mother with one child and living in County X could receive a daily living allowance rorn the welfare department of $40, which was reduced dollar-for-dollar by any earnings she might have had. In algebraic terms, where E = daily earnings, the welfare subsidy was calculated as follows: Daily subsidy = 40 - E Assuming she could earn $5 per hour, draw her daily budget constraint assuming she had 16 hours per day of available time. (b) Are there any circumstances in which a mother in County X who could earn $5 per hour would have chosen to work instead of receiving welfare? Explain