Magicwand started Masters degree in Operations Research

Magicwand · **#41**

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 :shock:

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

emeraldemon · **#42**

Looking more closely at your problem and what you call the solution, I think something is wrong, probably something is missing from your problem description. Was v defined in terms of x1,x2,x3 ? The values of x1,x2,x3 you suggest (if I'm interpreting you right) are [4/11,4/11,3/11], which gives v = -0.45455. But I can trivially come up with a better solution: x1 = x2 = x3 = 0, v = 0.

I don't really understand what you put with the grids of numbers, but it looks like maybe you are trying to solve a system of linear equations with Gaussian elimination? Linear programming is a different problem from solving linear systems, and it's harder. Was there a linear programming prerequisite for this class? You might not have the necessary background to do these, you may need to take some other class first.

Magicwand · **#43**

emeraldemon wrote:

Looking more closely at your problem and what you call the solution, I think something is wrong, probably something is missing from your problem description. Was v defined in terms of x1,x2,x3 ? The values of x1,x2,x3 you suggest (if I'm interpreting you right) are [4/11,4/11,3/11], which gives v = -0.45455. But I can trivially come up with a better solution: x1 = x2 = x3 = 0, v = 0.

I don't really understand what you put with the grids of numbers, but it looks like maybe you are trying to solve a system of linear equations with Gaussian elimination? Linear programming is a different problem from solving linear systems, and it's harder. Was there a linear programming prerequisite for this class? You might not have the necessary background to do these, you may need to take some other class first.

your trivial solution is not possible because this is LP for zero-sum game.
x1+x2+x3 have to equal to 1
if i solve that LP correctly answer would me 4/11,4/11,3/11
i want to know how.

i guess i will need to study linear programming all over again.
if you have any suggestion or even study materials so i can study... i would appreciate.
thank you for trying...

i have been at this for 3 nights straight...and no more strength left so i submitted it.

again thank you.

Uzziel · **#44**

http://www.youtube.com/watch?v=3dUphCwFDJA

Magicwand · **#45**

Uzziel wrote:

http://www.youtube.com/watch?v=3dUphCwFDJA

i saw couple of his video.... didnt learn anything new.
although i majored in math in college i realized that my understanding on math is so limited :oops:

i will attack that problem again after i finish STAT homework over the weekend...and another OR homework to stay ahead of the game.

Thank you all for your help.

i had enough of OR. now bash my brain with STAT :rambo:

cyclops · **#46**

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.

cyclops · **#47**

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 :shock:

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

Magicwand · **#48**

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.

really appreciate your help. i got full points by not showing work and using online game theory calculator but innocent looking problem shouldnt take me that long. i was disappointed at my math aptitude. again thank you.

Magicwand · **#49**

Operations Research Class:
first test was A, second test i bombed it (prob 50% or less), now i have to prep for final exam. only way for me to do well on this is solve all similar problem prior to the test. I will try to post all possible questions here hoping people help me solve them. (dont worry it is proctored exam so you are not solving my exam)

Statistical analysis: i expected to fail mid-term but i think i did better than i expected (guessing around 80%). this class count homework 40% of the grade... so if i do well on final i will be ok.

I wanted A and A but now my dream became realistic and hoping to receive B and B.
One more month of hard work and i will be done. Please pray for me. I can not do this by myself.

Thank you.

Magicwand · **#50**

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?

Magicwand · **#51**

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?

I have solved it. I have to use DOE with random number unchecked to get the correct output.
It took me many days of trial and error for me to get that and how do other students solve that questions??

Magicwand started Masters degree in Operations Research

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