Linear Programming: finding the feasibility region

[Lelia_A.]

Hi,

I am currently an independent study student, and I have searched around the web for any tutorial or help on how to approach my answer but cannot. If you can, please help me with some information on how to get my feasibility region.

I do know how to graph linear inequalities, but for some reason, I am having difficulty figuring out what part is the feasibility region so I can use the coordinates.

I have a problem below, and anyone who can show me how to locate the feasibility region, I would really, really appreciate it alot.

Find the coordinates of the ordered pair where the maximum value occurs for the equation P = 2x + 5y given these constraints.

x + 2y <= 8

3x + y <= 9

x >= 0

y >= 0

I know this will be in the first quadrant and change these inequalities to slope-intercept form for easier graphing (instructor says so). However, whatever I tried, it's not the same answer as what's given.

In addition, I also have another question. Whenever you graph an equation in slope-intercept form, and the slope is a negative, for example, -3/2, do you drop down three and over two times to the right?

I have been taught previously that you can rise up and down, but always run to the right. But my current instructor tells me that you can run right or left, but always rise up. In some ways, this is making me confused at what direction I should go when graphing.

Best,
Lelia Amber

 

[pka]

Here is a simple way to remember how slope works.
If you have a graph of the line, start at any point on the line.
Move one unit to the right (one horizontal unit), then to get back on the line if you have to move up then the slope is positive, moving down means negative slope.
I hope this helps you with this question.

 

[galactus]

Set the two upper equations equal and solve:

\(\displaystyle \L\\\frac{8-x}{2}=9-3x\)

\(\displaystyle x=2, \;\ y=3\)

That is a point.

The others can be gotten from the graph.

(2,3), (0,0), (3,0), (0,4)

It appears 2(0)+5(4)=20 is the max and 2(0)+5(0)=0 is the minimum.

 

[Lelia_A.]

Thanks! After working the problem myself and having that graph, I managed to find the shaded region. Well, I always did but I have no idea why I ended up with a different shaded area. Strange.

Your post has been very helpful, tq.

Lelia.