In your problemIf U = ln(G) + 4 ln(T)
where G is the number of hours spent playing golf and T is the number of
hours spent playing tennis. This person has 10 hours per week to devote to
these sports. However, each hour of playing tennis typically entails one hour
of waiting for an empty court, thus using up twice the time of actual play.
As a consequence, for example, if he spent 2 hours playing golf and 4 hours
playing tennis, he would have used up the full 10 hours of his available time.
a) What equation describes this person's time constraint?
So: 2T + G <or=10
b) What is the Lagrangian expression of this constrained maximization prob-
c) Use this Lagrangian expression to nd out the satisfaction (or utility)
maximizing choice of time to play golf and tennis.
The Lagrangian is
To maximise find where