The optimization problem below indicates a utility maximization problem for Emma, where $x1$ and $x2$ denote her demand for good $1$ and $2,$ respectively. Which of the following statements is not true?

$ma{x}_{x_1,x_2}0x_1^2{x}_2^3,$ subject $to2x_1+x_{2}10$

Emma's utility function is not concave but quasiconcave.

At $(x1,x2)=(1,2),$ Emma is willing to give up as much as $3$ units of good $2$ in order to obtain $4$ units of good $1.$

For utility maximization, Emma would consume $(x1,x2)=(2,6).$

The marginal utility of an extra dollar to Emma is $432$ utils.

When her income doubles, demand for good $1$ and $2$ both increase.