Exercise 3: (8+7+5) = 20

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".