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QUESTION $4$

The maximum value of the function $f(x,y,z)=x+2y+3z$ on the curve of intersection of the plane $x+y+z=1$ and the cylinder $x^2+y^2=1$ is

a$.3-\frac{\sqrt[\phantom{2}]{5}}{5}$

b$.3+\frac{\sqrt[\phantom{2}]{5}}{5}$

c$.3+\sqrt[\phantom{2}]{5}$

d$.3-\sqrt[\phantom{2}]{5}$

e$.4$