Consider the following small instance of the linear programming problem:
maximize 3x + 5y
subject to
x + y ≤ 4
x + 3y ≤6
x ≥ 0, y ≥ 0.
a. Sketch, in the Cartesian plane, the problem's feasible region, defined as the set of
points satisfying all the problem's constraints.
b. Identify the region's extreme points.
c. Solve this optimization problem by using the following theorem: "A linear programming
problem with a nonempty bounded feasible region always has a solution, which can be found at one
of the extreme points of its feasible region".
Fig: 1