You derive utility from Leisure (L) and your grade (G). The higher they are, the happier you are. Let your utility function be U(L,G). Your grade is increasing in your study time (S). You can therefore write G = f(S) where f is an increasing function describing how your grade relates to your investment in studying. It is the last day before the final exam and you have 24 hours to allocate between leisure and study. Write the optimization problem you are facing. You DO NOT need to solve it.
I'm confused with the equation I need to write. This is for a ECO micro class. Would the correct formula be:
max(L,G)
Subject to G = f(s)
Any and all help would be greatly appreciated. Thanks in advance.
The time constraint is $L+S=24$ (you can spend time on leisure or studying). Thus the problem is $$\max_{L,G} u (L, G) \\ \mbox{s.t. }\> L+S=24 \\ \> G= f(S)$$