Life In 19x19

Magicwand wrote:no taker for previous question..

now i have simpler problem..(i think)

max v
st
v ≤ 1/2 x1 - x2 - x3

v ≤ -x1 + 1/2 x2 - x3

v ≤ -x1 -x2 + x3

x1 , x2 , x3 ≥ 0

how do i solve above LP?
It has been so long i forgot how to solve.
thank you in advance..

Magicwand wrote:

Magicwand wrote:

emeraldemon wrote:Did your instructor suggest a method for solving linear programs? This problem is small enough that you should be able to test every vertex by hand, if that's all that's necessary.

can you guide me on how i can test every vertex?

i have similar example that is much simpler(with 2 variable) which was easily solved. one more variable throw me off.

I already have answer as [4/11,4/11,3/11] and try to figure how to derive that answer.
it shouldnt take this long for this simple problem but i am failing ....may be it is lack of sleep
i thought simple linear program i learned in college should do the trick...and done below using excel.

1/2 -1 -1 1
-1 1/2 -1 1
-1 -1 1 1

1 -2 -2 2
-1 1/2 -1 1
-1 -2 1 1

1 -2 -2 2
0 -1 1/2 -3 3
0 -4 -1 3

1 -2 -2 2
0 1 2 -2
0 -4 -1 3

1 0 2 -2
0 1 2 -2
0 0 7 -5

1 0 2 -2
0 1 2 -2
0 0 1 5/7

1 0 0 -3 3/7
0 1 0 -3 3/7
0 0 1 5/7

now that is not the answer i was looking for...
may be there is a mistake in my work or i am doing it totally wrong..
i would appreciate if someone can find my mistake.


v/r

cyclops wrote:

Magicwand wrote:no taker for previous question..

now i have simpler problem..(i think)

max v
st
v ≤ 1/2 x1 - x2 - x3

v ≤ -x1 + 1/2 x2 - x3

v ≤ -x1 -x2 + x3

x1 , x2 , x3 ≥ 0

how do i solve above LP?
It has been so long i forgot how to solve.
thank you in advance..

substitute x3 = 1 - x1 - x2 in the first two equations and you get v <= -1 + 3/2 xi ( i= 1 or 2 )
in the third equation it gives v <= 1 - 2x1 - 2x2

Because x1 and x2 play symmetrical rôles we expect x1 = x2 in the solution. Hence we have v <= -1 +3/2 x1 and v <= 1 - 4x1. Putting these equal we find x1 = 4/11. So the maximal v value is -5/11 for x1=x2=4/11 and x3=3/11. The details I leave to gladly you. I only have an outdated major in physics.

How would a mathematician solve it? He would put the three equations equal to 1 and solve for x1, x2 and x3. Finding a point x. He would draw a line through this point and the origin and intersect it with the plane x1+x2+x3 = 1 finding my (4/11, 4/11, 3/11 ) and my solution max(v) = -5/11. You don't need 7 hours if you try to visualize it. I wish I could apply the same wisdom to go.

Magicwand wrote:getting close to the end... thinks get harder and harder for me to figure out.
if anyone here knowledgable in minitab i need help on first question on attached.
It is not my exam question or homework question. It is a problem i downloaded that might appear in my final.
i think i have to get output with eight terms since it is 2^3.

8 terms are : Constant, A, B, C, A*B, ......A*B*C.
8 Effects for each terms:
8 Coef:
8 SE Coef:
8 T:
8 P:

can anyone explain how i can use minitab to get that output?