hw 2b

[Rachna Patel]

Anyone start this? I can't figure out what I'm doing wrong in the last steps. Attached is my excel spreadsheet. When I put this in solver I am getting a complete different answer of 0 mag ads and 50 TV ads which I think is wrong...

[Subramaniam Narayanan]

Cj	0	0	0	0	-1	-1
basis	x1	x2	x3	x4	a1	a2	bi
(0) x1	1	0	- 3/5	1/5	3/5	- 1/5	24
(0) x2	- 2/3	1	3/5	- 1/2	- 3/5	1/2	-14
zj	0	0	0	0	0	0
cj-zj	0	0	0	0	-1	-1		(-e=0)

should be,

(0) x2             0                     1                     1/5                 -2/5               -1/5                  2/5                  2

[Rachna Patel]

How did you get this new x2 row?

[Chase Morgan]

I got the new X2 row by multiplying the first row by -1/3 and adding it to row two (I got the same answer that was given by Rachna).

I have another question:

Here's what I get for the last tableau of Phase 1, and the 1st tableau of phase 2 (tableau 4). Tableau 4 doesn't seem right, as I work it every which way after this point and cant come to the same conclusion I came to using solver. Anyone else get this?

[Subramaniam Narayanan]

The bi for Tableau 3 should be 24 and 2

and in tableau 4, the Zj for column 3 should be (-1000)*(-0.6) + (-4000)*(0.2) = -200
and col 4 = (-1000)*(0.2) + (-4000)*(-0.4) = 1400
and -e = (-1000)*24 + (-4000)*2 = -32000

[Rachna Patel]

anyone meeting this weekend or do we still plan on doing this through email? I'm a bit lost with the sensitivity analysis and interpretation

[Maddy Fouts]

Has anyone started on hwk #3???

or done the write up for 2c

--

Madelaine G. Fouts
Class of 2011
Leavey School of Business

Santa Clara University

[Rachna Patel]

Hi Subramaniam,

Can you explain how you got 24 and 2 for tableau 3, or can you supply the excel spreadsheet if you used one so I can see the calculations?

Thanks,
Rachna

[Elliott Le]

Here are the calcs up to tableau 4. I got X1=24 and X2=2 as well, but in solver I got 30 and 0. Can I see someone's setup to see what I'm doing wrong?

Elliott Le

--
Elliott Le

[Sudha Venkatesh]

Elliott:

 

You should proceed to the next iteration since it has one positive value in Cj-Zj;

For the next iteration X2 is out of basis and  (X3,X1) in basis

then final values comes out as X1=30;x2=0(out of basis)

Hope it helps.

[Elliott Le]

That's where I got confused. 

I got 24/(-3/5) = -40 and 2/(1/5) = 10 in trying to find the pivot row. What happens when we get a negative value in this situation?

Elliott Le

--
Elliott Le

[Chase Morgan]

I asked the prof this same question and he responded with "get a study group".

Elliott Le

<Screen Shot 2011-10-14 at 8.05.07 PM.png>

<Screen Shot 2011-10-14 at 8.02.35 PM.png>

--
Elliott Le

--
Elliott Le

[Sudha Venkatesh]

Negative value means it fails to meet the constraint, hence we choose the positive value '10'.

[Sudha Venkatesh]

As suggested by a group member:

 

. -ve values on the Bi/pivot column  means nothing from an economical standpoint. Basically we want to know how far we go in one direction before violating a constraint. If the RHS is -ve we are already violating the constraint and hence cannot use that...

 

hope it helps

[Elliott Le]

Thanks.

--
Elliott Le

[Rachna Patel]

my report looks slightly different fom elliots. Does anyones match mine?

[Elliott Le]

My solver report's not right since I didn't rename some of the items.

Elliott Le

--
Elliott Le

[Darren Ng]

My report looks like Rachna's.

[Rachna Patel]

still struggling trying to get the bi to be 30,0

anyone have any ideas of what to do?

Also has anyone started on the last problem?

[Subramaniam Narayanan]

Take a look at my solution. Hopefully it will make things clearer...

[Gabriela Tchaga]

I got the same answers as Rachna and Subramaniam.

let me knwow if you guys have further questions. Thank you.

g

--
Gabriela G. Tchaga
GGTc...@gmail.com
510-386-5619

[Gabriela Tchaga]

anyone do 2c- question b for comparison?

[Gabriela Tchaga]

here is my solver for problem 3

[Victoria Cheng]

I got the same numbers as Gabriela.

[Chase Morgan]

As did I.

g

Elliott Le

Thanks.

Elliott Le

<Screen Shot 2011-10-14 at 8.05.07 PM.png>

<Screen Shot 2011-10-14 at 8.02.35 PM.png>

--
Elliott Le

--
Elliott Le

--
Elliott Le

--
Elliott Le

[Sidra Haider]

I have the same, but my fertilizer constraints was 

180X1+7

50X2  <

500,000

I get the same answer..

--
Sidra Haider
sidra....@gmail.com

[Victoria Cheng]

i had it both ways too...i guess it doesnt matter?....

[Carey Deangelis]

I have a question to Subramaniam's solution.  I was getting the same thing until I came to the bi.  For example: when I multiplied the row 2 in the first tableau by 1/3 I also multiplied the old row 2's bi by 1/3 making 30 and used that going forward.  Am I not suppose to do that?

Thanks,

Carey

On Sun, Oct 16, 2011 at 11:13 AM, Subramaniam Narayanan <ssnara...@gmail.com> wrote:

[Subramaniam Narayanan]

DOn't understand what exactly you did. Basically for row 2 in tableau 1, the row looks as follows:

 

   Cj    0   0   0   0   -1   -1

          X1 X2 X3  X4 A1 A2    bi

A1 -1  2   1   -1  0   1    0     50

A2  -1 1   3   0   -1   0   1     30

 

We now need to bring X2 into the basis and leave out A2. So row X2 col in the next tableao should have 0 1. To do that we first divide A2 by 3 and we will get:

 

X2 0    1/3 1 0   -1/3   0   1/2   30/3 (**)

 

30/3 = bi for the new row 2 which is = 10. Thats what I used in the next tableau.

[Carey Deangelis]

That makes complete sense to me.  So I was doing the right thing with the wrong number.  I was working with the 50 and the 10 that you get when you were working out to find which row will go out of the basis. 

Thank you for clarifying.

-Carey

[Gabriela Tchaga]

here is my write up for problem 3- d and e

Anyone have the write up for 2c so we can compare our answers?

Gabriela Tchaga

[Rachna Patel]

Is this right for 3c?

c. Explain in words exactly what each of the shadow prices mean:

Shadow price is the maximum price that the dairy farmer is willing to pay for an extra unit of a given limited resource.

 

Shadow price of land =0

The dairy farmer is not willing to pay for any extra for any acres of lands.

 

Shadow price of pumping = 2.74

The dairy farmer is willing to pay $2.74 more to pump one additional gallon of water.

 

Shadow price of fertilizer = 176.53

The dairy farmer is willing to pay $176.53 more to buy one more ton of fertilizer.

[Subramaniam Narayanan]

In the context of the problem the shadow price, I think, means how much the objective function is affected by a 1-unit change of each of the constraints, ie, how is the number of cattle-feed-days affected, if at all, by a 1-unit change of the constraint.
For example, the shadow price of pumping = 2.74, implies if the pumping capacity is increased by 1 gallon per day, the number of cattle-feed-days will increase by 2.74 days.

The objective function has no dependency on a $ value.

BTW, can someone confirm if the shadow price of fertilizer is 0.4836?

[Sudha Venkatesh]

what was ur idea on 3 d,e?

[Subramaniam Narayanan]

(d) Didn't think any assumptions of LP were violated, so we can use the model

(e) Given the constraints, the solution gives mgmt the best yield, so they should go ahead with the plan. However since shadow prices are also known, if additional pumping capacity and/or fertilizer capacity is made available, they should consider updating the plan to get e better yield...

[Rachna Patel]

Did everyone get a shadow price for fertilizer =  0.4836 or 176.53?

[Manuel Severino]

I got 2.74 and  0.4836 and I agree with Subramaniam on the solutions.


Manny

[Darren Ng]

For fertilizer, I got a shadow price of 176.53.

For (d), one could argue that the "certainty" assumption is violated, because the coefficients for fertilizer, yield, irrigation, etc are never known for certain. There are always external factors that are out of the farmer's control (weather, terrain, pests, etc). This is also stated in the slides from lecture 2, that certainty is almost always violated. I don't think any other assumptions were violated.

[Rachna Patel]

I just adjusted my input and got .4836 for shadow price.

[Manuel Severino]

If you use 180X1 + 750X2, then you have to convert the 250 tons of fertilizer to 500,000 lbs. I guess you could go the other way and convert everything to tons.

I guess as long as you use the same units across the board for that constraint, it should be all good.


Manny

On Mon, Oct 17, 2011 at 9:03 AM, Darren Ng <darr...@gmail.com> wrote:

[Subramaniam Narayanan]

While the argument for (d) holds, the bottom line is that this is not a stochastic problem - meaning though there is uncertainty we can still use the best guess and forecast info to use it in the model. As opposed to predicting portfolio returns which is completely undeterministic.

On Mon, Oct 17, 2011 at 9:03 AM, Darren Ng <darr...@gmail.com> wrote:

[Gabriela Tchaga]

hi--anyone do the write up to 2c that can send it so we can compare answers?