Consider the objective function $z=3x+4y$ subject to $4x+3y\le 24$, $3x+4y\le 24$, and $x,y\ge 0$. The objective function $z$ is maximized:

Find corner points of the feasible region defined by:$4x+3y=24$$3x+4y=24$$x=0,y=0$ Intersection of (1) and (2): Subtracting gives $x-y=0⟹x=y$. $7x=24⟹x=24/7$. Point is $(24/7,24/7)$.Corner points: $(0,0),(6,0),(0,6),(24/7,24/7)$.Value of $z=3x+4y$:At $(0,0):z=0$ At $(6,0):z=18$ At $(0,6):z=24$ At $(24/7,24/7):z=3(24/7)+4(24/7)=7(24/7)=24$.The maximum value $z=24$ is attained at two corner points $(0,6)$ and $(24/7,24/7)$.If the maximum occurs at two corner points, it occurs at all points on the line segment joining them. Thus, there are infinite points of maximization.