A Consumer Has a Budget Constraint Given By $p_{0} \widehat{x_{1}}+p_{1} x_{1}+p_{2} x_{2} \leq y$

Essay

A consumer has a budget constraint given by $p_{0} \widehat{x_{1}}+p_{1} x_{1}+p_{2} x_{2} \leq y$ where $p_{0}=5, p_{1}=0$ , $y=20, p_{2}=1$ . $\widehat{x_{1}}=1$ if positive amounts of $x_{1}$ are purchased and 0 otherwise. If the consumer has a utility function given by $U\left(x_{1}, x_{2}\right)=\left(x_{1}-13\right)^{2}+x_{2}$ , then how much of $x_{1}$ does the consumer purchase?