# Thread: Graphing a feasible Region?

1. ## Graphing a feasible Region?

from the linear example so far I have...

Profit = 20X + 16Y

and the constraints are:

X + 2Y ≤ 480
3X + 4Y≤1080

How do I show the Feasible Region and the Optimal Point on a graph.??

2. Originally Posted by bobchiba
from the linear example so far I have...

Profit = 20X + 16Y

and the constraints are:

X + 2Y ≤ 480
3X + 4Y≤1080

How do I show the Feasible Region and the Optimal Point on a graph.??
Hello bobchiba,

I'm assuming that $\displaystyle x \ge 0$ and $\displaystyle y \ge 0$.

Graph the two equalities:

$\displaystyle x+2y=480$ and $\displaystyle 3x+4y=1080$

Shade the appropriate regions indicated by the inequalities and find where they overlap. This is your feasible region.

Three of the vertices lie on the axes: (0, 0), (360, 0) , and (0, 240).

To find the 4th vertex, solve the two linear equations for their intersection point.

See attachment.

Then to find your optimal point or wher the profit function produces the largest value, substitute each vertex coordinates into your function and see what comes out.

3. Sorry I left out some of the constraints, they are all as follows:

X + 2Y $\displaystyle \le$ 480
3X + 4Y $\displaystyle \le$ 1080
X $\displaystyle \ge$ 60
Y$\displaystyle \ge$ 30

4. Do you have a question regarding the graph and instructions you've been provided? Thank you!

5. yes I sort of get what masters originally provided, but I forgot to mention that x and Y are not equal to zero, and its

X 60
Y 30

6. Okay; then follow the exact same graphing, corner-finding, and evaluating process outlined, but using your inequalities instead of the standard ones guessed in that earlier reply.

If you get stuck, please reply showing (or describing) your work and reasoning, clearly stating where you are having difficulty. Thank you!

7. Originally Posted by bobchiba
yes I sort of get what masters originally provided, but I forgot to mention that x and Y are not equal to zero, and its

X 60
Y 30
Well, bobchiba,

Withe these new constraints, the graph will look like this. Now find your vertices.