Prof. Hoffman in an article on "The Economics Sleep" in the June 1977 edition of the Journal of Political Economy specified a utility function for married couples recognizing the existence of females in microeconomic theory. U = U(Xw, Y w, Xh, Yh) (1)

Where X represents consumption, Y represents the fraction of 24 hours spent sleeping, W is wife, h is husband Let us assume that for a married couple in love the utility function can be specified as a multiplicative function to ensure marital stability (2)

U=XwYwXhYh

(2) While for a married couple not in love the utility function is specified as an additive function (3)

U=XhYw+XhYh

(3) Let us assume the wife and husband have the same taste; the utility functions (2) and (3) reduce to (4) and (5) respectively. (4) X^2Y^2 (5)U=2XY Given a budget constraint X = w(l-Y) where w is the wage rate, determine the optimal number of hours of sleep for the two different couples.