simplex method: minimize f = 4x + y subject to....

[Goods]

I am trying to solve a problem using the 'symplex method' and have no clue. I was hoping someone could help. Thank you in advance.

Here is the problem:

Use the simplex method to minimize f = 4x + y

. . .-x + y < 4
. . .3x + y > 12
. . .x + y < 20
. . .x > 0
. . .y > 0

 

[stapel]

I am trying to solve a problem using the 'symplex method' and have no clue.

Are you saying that the Simplex Method has not been covered in class, so you're needing links to lessons on the topic?

Thank you.

Eliz.

 

[Goods]

I will take any help I can get. Thank you!

 

[Goods]

Ok, I graphed it by hand and got this;

Min=14
x=2
y=6


Does that look right, or can you show me where I may have made my mistake

 

[skeeter]

I graphed the region also and got a quadrilateral. I get its corners to be
(2,6)
(8,12)
(4,0)
(20,0)

for f = 4x+y ...

4(2) + 6 = 14 ... min
4(8) + 12 = 44
4(4) + 0 = 16
4(20) + 0 = 80 ... max

 

[JakeD]

Ok, I graphed it by hand and got this;

Min=14
x=2
y=6


Does that look right, or can you show me where I may have made my mistake

Solving by graphing is not the Simplex Method, which is what the problem asks you to use.

Here is a Simplex Method Solver which will take you through all the steps of a solution. It has some description of the method, but not a full description. For that, you will need a textbook.

 

[galactus]

With these linear programming problems, it may help to graph the lines. Set your inequalities to equalities and graph.