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.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!