SOLUTION: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT Maximize p = x + y subject to x

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Question 1112478: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT
Maximize p = x + y subject to
x + 2y ≥ 30
2x + 2y ≤ 30
2x + y ≥ 30
x ≥ 0, y ≥ 0.
p=
(x, y)=

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.

The feasibility region is empty; so nothing can be optimized.
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
The constraining lines  are shown in the Figure below:





Plots x + 2y = 30 (red),  2x + 2y = 30 (green)  and  2x+y = 30 (blue)



The feasibility area, according to the condition, is the area of the first quadrant 

    - above the red line,

    - below the green line,

    - above the blue line.


It is easy to see from the plot that this set is empty.

Answer. The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

--------------
On solving minimax problems by the LP-method see the lesson
    - Solving minimax problems by the Linear Programming method
in this site.


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