Maximise utility with the Lagrange method in this case.
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.