Linear optimization problem. Infeasible, Unbounded, or Multiple Solutions?

erikafuuko

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Apr 6, 2016
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Can you tell me if the linear programming problem exhibits infeasibility, unboundedness, or alternate optimal solutions?

Minimize:
1x + 1y

Constraints:
5x + 3y ≤ 30

3x + 4y ≥ 36

y ≤ 7

x , y ≥ 0

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I've graphed this on paper just to see if there would be a potential feasible region. So far, I only see some regions where two of the main constraints overlap, but there is not a single region where all of the constraints overlap for a feasible region. Could this linear optimization problem have an infeasible solution?
 
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