Question

Find the maximum and minimum values of the function f(x,y,z)=x+2y subject to the constraints y2+z2=361 and x+y+z=5

Answer 1

Apply lagrange multiplier: \[f(x,y,z)-\lambda _{1}(g(x,y,z)-k)-\lambda _{2}(h(x,y,z)-k)\]
Partial derivatives with respect to x,y,z, lambda1, lambda2. Then solve for x,y and z and find if the critical points are maximums or minimums