Question 1141944: 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 math_helper(2461)   (Show Source):
You can put this solution on YOUR website! When you graph the three inequalities,
3x + 5y ≥ 20
3x + y ≤ 16
−2x + y ≤ 2
You will get a feasibility region in the shape of a triangle (the triangle is located in Q1 so x>=0 and y>=0 hold). The corners of the triangle are at:
(2.8,7.6)
(5,1)
(0.769,3.538)
Evaluating these (x,y) values in P = 5x + 4y gives:
(2.8,7.6) 5x + 4y = 44.4 <<< max @ (2.8,7.6)
(5,1) 5x + 4y = 29
(0.769,3.538) 5x + 4y = 17.997 <<< min @ (0.769,3.538)
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EDIT: Added the Desmos graph (picture) below...
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