Consider a one$-$period static consumption$-$leisure model. Suppose the individual has the following utility function over consumption $c$ and leisure $l$: $U(c,l)=ln(c)+1\mathrm{.}5l.(1)$ The individual$s$ budget constraint $is$ given $by$: $c=(1-t)wn,$ where $tis$ the tax rate, $wis$ the real hourly wage rate, and $nis$ the number $of$ hours worked. The total available time $is$ normalized $to1,sol=1-n.(a)$ Set $up$ the Lagrangian for the problem. $[1](b)$ Verify that the consumption$-$leisure optimality condition $is$ equal $to$ the negative slope $of$ the budget constraint. $[2](c)$ Solve for the optimal values $of$ leisure, labor, and consumption. $[2]$