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retrolina

Member

Registered: 2016-10-02

Posts: 4

Linear programming - maximization or minimization?

Hi everyone,

I'm doing a unit in quantitative modeling and we jus got the answer sheet for our completed mid semester test. I am no expert at this stuff, but I think my professor has given the wrong answer (!).

This was our question:

The following is a graph of a linear programming problem. The feasible solution is shaded, and the optimal solution is at the point labelled Z*.

This linear programming problem is a(n)

a)    Maximization problem
b)    Irregular problem
c)    Minimization problem
d)    Cannot tell from the information given

I would say it's a minimization problem, but the prof is saying maximization.

Can anyone please clarify.

Thank you

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear programming - maximization or minimization?

Hi;

Can you reconstruct the constraints from that diagram?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

retrolina

Member

Registered: 2016-10-02

Posts: 4

Re: Linear programming - maximization or minimization?

Hi bobbym,

I am afraid that was all the information that was given.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear programming - maximization or minimization?

Hi;

The only thing I can come up with is this

Minimize x + y

Subject to:

x + y <= 10
x >= 0
y >= 0
x + 2 y >= 8
2 x + y >= 8
x + y >= 6

The answer is 6 when (4,2) so that Z* point is a minimum and this is a minimization problem. But there could be other formulations maybe? So, I disagree with your professor and what else is new? When do I ever agree with those fellows? Of course, they never agree with me either...

I guess the only solution is to drop us all off in the jungles of Florida, fully armed and ready to fight to the death. The survivor ( which will be me of course ) is the one who is right. Worked for the Norseman.

This looks like just the place and it is only about 2 miles from where I am sitting right now. I could be there in 15 minutes, ready to rumble.

Does this sound farfetched? Perhaps even a bit barbaric...Back in the past mathematicians would sometimes fight duels rather than engaging in wimpy intellectual debates. One story in particular, the great Tycho Brahe who lost his nose while fighting a duel to decide which man was the better mathematician. Tycho, may have lost his nose but the other fellow was heard from no more. Back in the days of the great Italian EM guys you would quickly lose an eye or an ear if you accused one of them of being unable to solve certain cubics.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

retrolina

Member

Registered: 2016-10-02

Posts: 4

Re: Linear programming - maximization or minimization?

Thanks for your answer. I am challenging my professor It is actually really obvious that either A or J will give you a higher value regardless of what combination of coefficients you use.... as will many non-extreme points within the feasible region. Embarrassing!

If he doesn't increase my grade then perhaps I will challenge him to a duel!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear programming - maximization or minimization?

Yes, we need more duels in math, like in the good old days. Make sure you protect your nose, just to be on the safe side.

I am challenging my professor

That will be easy, if he shows you an example where Z* is a maxima you can show him mine as a  counterexample.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Linear programming - maximization or minimization?

Hi;

The only thing I can come up with is this

Minimize x + y

Subject to:

x + y <= 10
x >= 0
y >= 0
x + 2 y >= 8
2 x + y >= 8

The answer is 15 / 3 when (8/3,8/3) so that Z* point is a minimum and this is a minimization problem. But there could be other formulations maybe? So, I disagree with your professor and what else is new? When do I ever agree with those fellows? Of course, they never agree with me either...

I guess the only solution is to drop us all off in the jungles of Florida, fully armed and ready to fight to the death. The survivor ( which will be me of course ) is the one who is right. Worked for the Norseman.

This looks like just the place and it is only about 2 miles from where I am sitting right now. I could be there in 15 minutes, ready to rumble.

Does this sound farfetched? Perhaps even a bit barbaric...Back in the past mathematicians would sometimes fight duels rather than engaging in wimpy intellectual debates. One story in particular, the great Tycho Brahe who lost his nose while fighting a duel to decide which man was the better mathematician. Tycho, may have lost his nose but the other fellow was heard from no more. Back in the days of the great Italian EM guys you would quickly lose an eye or an ear if you accused one of them of being unable to solve certain cubics.

But why the point E (8/3,8/3) is not in the shaded region?Or in other words why  the shaded region does not extend upto E? What is the significance of the line x+y=6 ?

Last edited by thickhead (2016-10-03 17:08:08)

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear programming - maximization or minimization?

Hi;

All fixed with Z* as the minimum, so it is still a minimization problem.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

retrolina

Member

Registered: 2016-10-02

Posts: 4

Re: Linear programming - maximization or minimization?

Update: my professor finally realised that he was wrong. Victory! My grade goes up 1 point. YAY

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear programming - maximization or minimization?

Did you see my fix? But it does not change the result, it was still a minima.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Linear programming - maximization or minimization?

It is really a strange problem.Object is to minimize x+y; There are 2 constraints for the same x+y and the optimum point is any point between (2,4) and (4,2).

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear programming - maximization or minimization?

I never saw one like that.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.