Min has a utility function defined over consumption (C) and fun (F) of the following form U = C + CF + F. Min has T hours in the day to either spend working at wage, w, or having fun. She spends all her earnings, and her non-labor income (N) on consumption which costs a dollar a unit.

Use the Lagrangian multiplier method to find Min's optimal amount of fun as a function of the parameters of the problem.