Question:
Let U(x,y)= Ax^ay^b be the utility function of an individual. The individual has x hour leisure time per day and consumers y units of other goods. The individual works and is paid w $ per hour. The average price of the other goods is p $. We assume that the individual spends his/her total income i.e.
py = w(24 - x)
Use the Lagrange method to determine how many hours this individual works per day to maximize the utility.