Find the maximum value of P = 5x + 6y
subject to the following constraints:
( x + y = 6
2x + 3y = 16
x>0
y>20

9514 1404 393

  34

Step-by-step explanation:

The graph shows the vertex of the feasible region that is farthest from the origin is (2, 4). These are the values of (x, y) that maximize P.

  P = 5(2) +6(4) = 10 +24 = 34

The maximum value of P is 34.

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Additional comment

The feasible region is entirely contained within the first quadrant. We have left off the x ≥ 0 and y ≥ 0 constraints to leave the inequalities uncomplicated.

The graph shows the line 34 = 5x +6y so you can see that it only intersects the feasible region (doubly-shaded area) at the vertex where the objective function is maximized.

this is false ^.^ lol