SOLUTION: 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

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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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