Question 549802
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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 *[tex \Large x\ +\ y\ =\ 5] in the interval *[tex \Large 0\ \leq\ x\ \leq\ 2.5] 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
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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