$3\mathrm{.}1$ Utility Maximization A consumer allocates their income M $=60$ between two goods, Good $1$ and Good $2,$ with prices p$1=4$ and p$2=6,$ respectively. The consumer$$s preferences are represented by the utility function: U$($x$1,$ x$2)=$ x $0\mathrm{.}71$ x $0\mathrm{.}32.$ Tasks: $1.$ Set up the budget constraint. $2.$ Find the optimal bundle of quantities x $1$ and x $2$ using either one of the following two methods: : $$ Marginal Rate of Substitution $($MRS$)$ equals to price ratio. $$ Lagrangian method. $3.$ Calculate the maximum utility the consumer achieves with that optimal bundle.