Hi k9queen!
Let's call, as you mentioned in your question:
X1 = Quantity of A in Regular
X2 = Quantity of A in Supergro
X3 = Quantity of A in Jungle Feeder
X4 = Quantity of B in Regular
X5 = Quantity of B in Supergro
X6 = Quantity of B in Jungle Feeder
So the function you set to minimize in QM is not correct: you
multiplied X2 by 0.5, when X2 means "quantity of A in Supergro", and
component A costs 0.3 and not 0.5. The correct equation to minimize
is:
0.3*X1 + 0.3*X2 + 0.3*X3 + 0.5*X4 + 0.5*X5 +0.5*X6
Now let's get to the constraints. One of the restrictions is that
there must be 1000 pounds of Regular and 2000 pounds of *each* of the
other two. Assuming that the amount of pounds of Regular equals the
sum of the amount of components A and B in Regular (and the same goes
for the other kinds fertilizer), we have the following set of
constraints:
X1 + X4 = 1000
X2 + X5 = 2000
X3 + X6 = 2000
The other restriction is with respect to nitrogen and phosphorous
contents in each of the fertilizers. Let's see what would be the
formula to determine these contents as a function of the quantity of
its components. Basically, the nitrogen (phosphorous) percentage in a
fertilizer is a weighted average of the nitrogen (phosphorous)
percentage of its components. Say for example, that we mix 500 pounds
of A with 500 pounds of B to produce 1000 pounds of fertilizer. Since
component A accounts for half the total amount of fertilizer, and
component B accounts for the other half, we would have the the
nitrogen percentage in this fertilizer is:
(500/1000)*14 + (500/1000)*20
= (1/2)*14 + (1/2)*20
= 17
So a fertilizer created in this way would have 17% of nitrogen.
Similarly, it would have 21% of phosphorous. Similarly, if it had 600
pounds of component A and 400 of component B, the nitrogen percentage
would be:
(600/1000)*14 + (400/1000)*20
= 16.4
The nitrogen percentage would be 16.4% in this case. So the general formula is:
Nitrogen % = (Amount of A / 1000)*14 + (Amount of B / 1000)*20
Phosphorous % = (Amount of A / 1000)*18 + (Amount of B / 1000)*24
Therefore, the constraints become:
X1*(14/1000) + X4*(20/1000) >= 10
X1*(18/1000) + X4*(24/1000) >= 16
X2*(14/1000) + X5*(20/1000) >= 12
X2*(18/1000) + X5*(24/1000) >= 20
X3*(14/1000) + X6*(20/1000) >= 15
X3*(18/1000) + X6*(24/1000) >= 18
When writing this problem of 6 variables and 9 constraints into QM, I
got the following answer:
A (pounds) B (pounds)
Regular 1000 0
Supergro 667 333
Jungle F 833 167
(the number were rounded)
I hope this helps! If you have any doubts regarding my answer, please
don't hesitate to request a clarification before rating it. Otherwise
I await your rating and final comments.
Best wishes!
elmarto |
Request for Answer Clarification by
k9queen-ga
on
04 Dec 2003 12:11 PST
Hi Elmarto,
Could you please look @ question #283068 - and see if you can answer
these for me. It is still open.
Thanks!
|
Clarification of Answer by
elmarto-ga
on
04 Dec 2003 13:14 PST
Hi k9queen!
I've noticed that in question #283068, politicalguru-ga has already
pointed you to a site with the answers to your questions. Could you
please specify what information do you need besides that which is
already stated on the page? More detailed answers perhaps?
Thanks a lot,
elmarto
|
Request for Answer Clarification by
k9queen-ga
on
05 Dec 2003 09:13 PST
Hi Elmarto,
Yes, I need more details if possible, and the graphs.
Also, I have a question from the fetilizer question you answered.
I will post it under appropriate question. The solution isn't working :(
|
Request for Answer Clarification by
k9queen-ga
on
05 Dec 2003 09:20 PST
Sorry I hit the post request button too soon.
This solution is not fitting, I think the error might be from using
1000 pounds for all three fertilizers instead of 2000 for the last
two. Anyway, in order to get QM to work and get a solution, I put in
the % of the nitrogen and phosphorous and used the % of nit. & phos.
as a portion of the weight needed. In order to get x1 and x2 etc.,
just change the top row (where is says Comp A-Reg etc.) to x1, x2
etc., and on the side (where it says Pounds of regular etc.) change to
contraint 1, and constraint2 etc.
The solution then is total cost $1700. With reular using 100% of
comp. A, supergro using 1333.33 lbs. of comp A, and 666.67 lbs. of
comp B, jungle feeder using 1666.67 of comp A and 333.33 lbs. of comp
B.
Does this make sense?
|
Clarification of Answer by
elmarto-ga
on
05 Dec 2003 10:19 PST
Hi k9queen,
You're absolutely right, there is a mistake in my answer. I'm very
sorry. The error is exactly where you mention: I forgot to use 2000
instead of 1000 for the last two types of fertilizers. When this is
corrected, the answer QM gives is the one you mention in the Request
for Clarification.
Again, I'm very sorry and I hope this error didn't cause you much
trouble. I'll try to answer your other question as soon as possible.
Best wishes!
elmarto
|
Request for Answer Clarification by
k9queen-ga
on
06 Dec 2003 16:05 PST
Hi Elmarto,
Any luck with the question that politicalguru
started? I have noticed that it has "been
currently worked on" and then back to its opne status
a couple of times.
|
Clarification of Answer by
elmarto-ga
on
07 Dec 2003 16:21 PST
Hi k9queen!
I've just finished answering that question! I had some trouble with
the graphics but they are working fine now.
Cheers!
elmarto
|
