Consider the following Linear Programming problem:

Max z = 69 x 7 y

where the decision variables are subject to the constraints:

23 x 19 y 1150

x + 3 y 138

x + 5 y 150

x 0

y 0

Fill in the extreme points that define the feasible region in counterclockwise order:

P1(0, 0), P2(50, 0), P3( _____ , ______), P4( ______ , _____), P5(0, ______ )

Answer:

4. The theory of Linear Programming indicates: the maximum and minimum values of the objective function occur at the extremes of the feasible region when it is bounded and not empty. And therefore, to find the optimal points (maximum or minimum), it is enough to compare the evaluations of the objective function at the extreme points. Continuing with the previous problem: 1) Indicate the value of z at the maximum. 2) Suppose that the previous problem were to minimize, indicate the value of z at the minimum. Answer: