Given the objective function:

$\displaystyle {f}={6}{x}+{9}{y}$

Draw the boundary to the feasible region corresponding to the constraints

$\displaystyle {\left\lbrace\begin{array}{c} {y}+{x}\le{5}\\{y}+{2}{x}\le{6}\\{x}\ge{0}\\{y}\ge{0}\end{array}\right.}$

If this region is unbounded use the necessary points from the constraints and $\displaystyle {\left({11},{0}\right)},{\left({11},{11}\right)},{\left({0},{11}\right)}$ to show the an unbounded region.



Then use the feasibility region above to find the maximum and minimum of the given objective function.

Maximum: (If needed, separate points with a comma. Use DNE if the value does not exist.)

Minimum: (If needed, separate points with a comma. Use DNE if the value does not exist.)