min 2x+y subject to: x+y+z=1 and y^2+z^2=4

Question

Any help would greatly be apprecaited.

y^2+z^2=4 --->

put y = 2 cos(theta) and

z = 2 sin(theta)

x+y+z=1 ---->

x = 1-2(cos(theta) + sin(theta))

2x + y =

2 - 2 cos(theta) - 4 sin(theta)

It's not difficult to find the minimum of this function!

You can also use lagrange multipliers...