1. Find the maximum and minimum values of subject to the constraint .
2. Find the maximum and minimum values of subject to the constraint .
3. Find the maximum and minimum values of subject to the constraint . Assume that for this problem. Why is this assumption needed?
4. Find the maximum and minimum values of subject to the constraint .
5. Find the maximum and minimum values of subject to the constraint .
6. Find the maximum and minimum values of subject to the constraints and .
7. Find the maximum and minimum values of subject to the constraints and .