Science:Math Exam Resources/Courses/MATH200/December 2012/Question 04/Hint 2

To handle the boundary case, break up the boundary into 4 cases: $\displaystyle x=-1$, $\displaystyle x=3$, $\displaystyle y=-1$, and $\displaystyle y=1$. For the first line, you get a new function $\displaystyle g(y)=f(-1,y)$, which you can then optimize subject to the constraint $\displaystyle -1\leq y\leq 1$. The other lines are similar.