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## #1 2006-01-09 00:39:33

siretfel
Member
Registered: 2006-01-09
Posts: 1

### Linear Programming (maximization)

The problem is as this:

You have company A that produces blue (20 tons) and yellow (16 tons ) paint. You can also produce green paint by an analogy of 2:1 i.e. 2 tons of blue and 1 ton of yellow gives 3 tons of green paint. Company A can only produce maximum of 6 tons of green though.

You can sell each ton of paint  by 100 dollar per ton. A company B can buy from you 8 to 10 tons of paint by an analogy of 2:2:1, i.e. 2 blue 2 yellow 1 green = 10 tons.

The problem is to find the maximum profit company A can make, i.e. (max) profit=120B+120Y+120G
and this requires to find the restrictions first.

Any help would be welcome cause the 'analogies' REALLY confuse me a lot!! (I mean the 2:2:1 etc etc)

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## #2 2006-01-09 11:52:49

4littlepiggiesmom
Member
Registered: 2006-01-09
Posts: 42

### Re: Linear Programming (maximization)

Not sure if all this is right but I get after they've made their 6 tons of green that
they have 16 tons of blue left and 14 tons of yellow!

So when they sell they will sell 4 tons of blue + 4 tons of Yellow + 2 tons of green! for \$1000

This leaves them 12 tons of  blue + 10 tons of yellow and 4 tons of green; so if they could they could sell adnother of the 10 ton set and end up with 4 blue and 2 yellow letft...
Hope this is what you need and if not sorry! H

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## #3 2006-01-09 15:03:31

Member
Registered: 2005-11-28
Posts: 97

### Re: Linear Programming (maximization)

well, I am confused right away by your objective function...
Why are you maximizing 120B+120Y+120G ?
Since you are selling the paint at \$100 per ton, shouldn't it be max 100B+100Y+100G ?
and I'm not sure, but your constraints might need to look like this:
(note: The inequalities here are not strict...so when I use <, I actually mean less than or equal to)
2B+Y < 6
2B+2Y+G > 8
2B+2Y+G < 10
B,Y,G > 0

If this looks like it makes sense, I can help you solve it...If I have misunderstood, I apologize...and please clarify

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
-Bertrand Russell

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## #4 2006-01-09 17:32:53

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Linear Programming (maximization)

6 green, 12 blue, 12 yellow makes 30 out of 36.
So sell three lots of 10 to sell 30 tons.
\$3000
Drawing a graph was helpful.   y=20-2x,   y= 16-x ,   y=3x,  for x between 0 and 2.

igloo myrtilles fourmis

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