- (5 points) Use Newton-Raphson to determine the extreme points of the following function. $$ f(x1, x2)=... $$ Hint: use (−, −) and (−, −) as starting points and write − iterations.
- Consider the problem
$$
\text{Maximize }
f(x,y,z)= ...\
\text{subject to }
\begin{cases}
g_1(x, y, z) = ... = 0\
g_2(x, y, z) = ... = 0
\end{cases}
$$
- a. (4 points) Use Jacobian method to solve the problem using x and y as dependent variables and apply the sufficient condition to determine the type of the resulting stationary point.
- b. (1 point) Determine the sensitivity coefficients given the solution in previous part.
- c. (5 points) Verify your answers for previous parts using Lagrangian method.
- (5 points) (Extra points) Use the sufficiency condition to identify the extreme points. $$ f(x,y)=... $$