SOLUTION: Sorry, I pressed the wrong button before... I am lost can someone help with this; Given the restraints x + y <=5 y >= x

Question 549802: Sorry, I pressed the wrong button before...
I am lost can someone help with this;
Given the restraints x + y <=5
y >= x
x >=0
and the objective Function C = x + y, find the maximum value?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given the restraints x + y <=5
y >= x
x >=0
and the objective Function C = x + y, find the maximum value?
----
Graph the line y = x
Shade the area above the line
----
Graph the line y = -x+5
Shade the area below the line
---
Shade the area to the right of x = 0 that is above y = x
and below y = -x+5.
---
Find the coordinates of the three vertices of the resulting
triangle: (0,0) ; (0,5), (2.5 , 2.5)
---
Evaluate C = x + y for each of those number pairs:
(0,0): C = 0
(0,5): C = 5
(2.5 2.5) C = 5
------------------------
Max for (0,5) and for (2.5 , 2.5)
====================================
Cheers,
Stan H.
===============

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Graph your three constraint inequalities on the same set of coordinates. The area where the three solution set regions overlap, in this case a triangle with vertices (0,0), (0,5), and (2.5,2.5) is the area of feasibility. A linear programming theorem states that if an optimum exists it is at a vertex of the feasibility polygon.

In this case, two of your vertices, namely (0,5) and (2.5,2.5) give the same objective function value, namely 5. That means any point on the line in the interval optimizes the objective.

Any time the boundary of one of your constraint inequalities has the same slope as your objective function, you will likely get into the situation of not having a unique answer.

John

My calculator said it, I believe it, that settles it

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