I am struggling to solve this optimization problem using KT, because it is way harder than those that I dealt with in the past. I would appreciate it if someone kelps me with this one.
$$ \max _{c, n, e} f(c, n, e)=\max _{c, n, e}\left\{\ln (c)+\theta \ln \left(n+a_{1}\right)+\lambda \ln \left(e+a_{2}\right)\right\} $$
Where $c \geq 0, n \in\left[0, \frac{1}{\phi}\right], e \geq 0$ are continuous choice variables and $\phi>0, \theta>0, \lambda>0, a_{1}>$ $0, a_{2}>0$ are parameters. Maximization is subject to the constraint: $$ c=w(1-\phi n)-e p+R $$