The economy of Northern Saskatchewan is in equilibrium when the system of equations $2xz+xy+z-2\sqrt[\phantom{2}]{z}=11$ and $xyz=6$ is satisfied. One solution of this set of equations is $(x^{**},y^{**},z^{**})=(3,2,1)$ and the economy is equilibrium at this point. Suppose that the prime minister discovers that the variable $z$ can be controlled by a simple decree.

a$.$ If the prime minister raises $z$ to $1\mathrm{.}1,$ use differential calculus to estimate the change in $x$ and $y$ simultaneously.

b$.$ If $x$ were in the control of the prime minister and not $y$ or $z,$ explain why you cannot use this method to estimate the effect of reducing $x$ from $3$ to $2\mathrm{.}95.(20$ points$)$ Use handwriting please do not use ai this is mathematical economics question