Question 1141999: Solve the linear programming problem by the method of corners.
Find the minimum and maximum of P = 5x + 4y subject to
3x + 5y ≥ 20
3x + y ≤ 16
−2x + y ≤ 2
x ≥ 0, y ≥ 0.
The minimum is P =
at
(x, y) =
.
The maximum is P =
at
(x, y) =
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! using the desmos.com calculator, you would graph the opposite of the constraint inequalities
the constraints are:
3x + 5y ≥ 20
3x + y ≤ 16
−2x + y ≤ 2
x ≥ 0
y ≥ 0
you would graph:
3x + 5y <= 20
3x + y >= 16
−2x + y >= 2
x <= 0
y <= 0
the graph looks like this.
the area of the graph that is not shaded is your region of feasibility.
the corner points of that region are where the maximum / minimum value of the objective function lies.
the objective function is p 5x + 4y
the corner points on the graph are:
(2.8, 7.6)
(.769, 3.538)
(5, 1)
these results are in (x,y) format.
evaluation of 5x + 4y for each yields.
(2.8, 7.6) results in 44.4
(.769, 3.538) results in 17.997
(5, 1) results in 29
the maximum value is 44.4 at (2.8, 7.6)
the minimum value is 17.997 at (.769, 3.538)
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