Consider the following optimization problem:

- Sketch (draw a picture) the feasible set and the level set of the objective function.
- Write down the Lagrange multiplier condition.

Consider the following optimization problem:

- Write down the Lagrange multiplier condition.
- Does this optimization problem has finite optimal solution? Why?

Consider the following optimization problem:

- Write down the Lagrange multiplier condition.
- Find the point satisfying the condition and find the corresponding Lagrange multiplier.
- For each point satisfying the condition, determine whether it is the optimal solution.