$5.$ Phoebes utility function is given by U$($L$,$ C$)=$ C$($L$+8).$ There are $16$ hour in a day. Her wage as a server is $$10/$hr$.$ and she gets $$40$ non$-$labor income from playing her guitar. $(1$ point each$)$a$.$ Find the budget constraint and then the optimal number of hours she should spend in Leisure $($L$).$ b$.$ Is it possible for Phoebe to consume $$100$ and have $12$ hours of leisure? Explain. c$.$ If the wage changed to $$5/$hr would Phoebe work more or less? Are Leisure and Consumption gross complements or substitutes? d$.$ Using the optimal amount of work from parts a and c$,$ what is the elasticity of Phoebes labor supply? Is her labor supply elastic?