Chemical Engineers ? Good at Maths? Help with question on optimization needed

#1
Hopefully someone can help with this linear programming question

Any Chemical Engineers / Maths guys on ?

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A chemical plant makes three products (E, F and G) and utilises three raw materials (A, B and C) in limited supply. Each of the three products is produced in a separate process (1, 2 and 3) as shown in the diagram.


The available materials A, B and C do not have to be totally consumed. The reactions involving A, B and C are as follows:


Process 1: A + B = E
Process 2: A + B = F
Process 3: 3A + 2B + C = G
Raw Material Maximum Available, kg/day Cost pence/kg
A 30,000 1.5
B 20,000 2.0
C 15,000 2.5


Process Product Reactant Requirements (kg) per kg product Processing Cost Selling price of product
1 E 2/3 A, 1/3 B 1.5 pence/kg E 4.5 pence/kg E
2 F 2/3 A, 1/3 B 0.5 pence/kg F 3.9 pence/kg F
3 G 1/2 A, 1/6 B, 1/3 C 1.0 pence/kg G 3.0 pence/kg G


NB. Mass is conserved

It is required to formulate this as an optimisation problem. Set up and identify:

An objective function to maximise the total operating profit per day
Equality Constraints
Inequality Constraints
You are not required to solve this problem.
GLASGOW CELTIC - CHAMPIONS 2006-2007
#3
Ah, simplex algorithms. I can do them but they take long and are hard.
Is it still a God Complex if I really am God?

America is the only country that went from barbarism to decadence without civilization in between.
Oscar Wilde
#4
Quote by Meths
Ah, simplex algorithms. I can do them but they take long and are hard.



Any help you can give would be most appreciated
GLASGOW CELTIC - CHAMPIONS 2006-2007
#5
Quote by mabozar
Hopefully someone can help with this linear programming question

Any Chemical Engineers / Maths guys on ?

--------------------------------------------------------------------------------

A chemical plant makes three products (E, F and G) and utilises three raw materials (A, B and C) in limited supply. Each of the three products is produced in a separate process (1, 2 and 3) as shown in the diagram.


The available materials A, B and C do not have to be totally consumed. The reactions involving A, B and C are as follows:


Process 1: A + B = E
Process 2: A + B = F
Process 3: 3A + 2B + C = G
Raw Material Maximum Available, kg/day Cost pence/kg
A 30,000 1.5
B 20,000 2.0
C 15,000 2.5


Process Product Reactant Requirements (kg) per kg product Processing Cost Selling price of product
1 E 2/3 A, 1/3 B 1.5 pence/kg E 4.5 pence/kg E
2 F 2/3 A, 1/3 B 0.5 pence/kg F 3.9 pence/kg F
3 G 1/2 A, 1/6 B, 1/3 C 1.0 pence/kg G 3.0 pence/kg G


NB. Mass is conserved

It is required to formulate this as an optimisation problem. Set up and identify:

An objective function to maximise the total operating profit per day
Equality Constraints
Inequality Constraints
You are not required to solve this problem.


Seems easy enough to me...
#6
The Pit: a place that you can ask to do your homework for you...

Seriously, do it yourself.
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#7
Figured it out, but I cant post it here as showing all the work takes too many characters, so I posted it here: LINK
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$100 obo
Message for negotiaton.
#8
Quote by penguin-pirate
Figured it out, but I cant post it here as showing all the work takes too many characters, so I posted it here: LINK

I see what you did there.

You have learned well, young padawan.
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╔═╗
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╚═╝
Always outnumbered, never outgunned...
#9
Well I don't remember how to do it... but to encourage you I assure you that this is really easy
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Lyke omg D@ @p0OcpLpSYe.
#10
Quote by i have to pee
I see what you did there.

You have learned well, young padawan.


Thank you.
Sig space for rent.
$100 obo
Message for negotiaton.
#11
Quote by i have to pee
The Pit: a place that you can ask to do your homework for you...

Seriously, do it yourself.



Been working on it for 2 days and ahm just struggling with a part of it. Felt it was worth seeing if anyone could help me as I cant take it any further.

I thought that was what the internet and forums with other people were for (sharing info on anything) but I am mistaken its about sad individuals ripping the piss and dreaming about chewbacca.
GLASGOW CELTIC - CHAMPIONS 2006-2007
#12
oh **** lol I'm sorry I didn't notice the subtle joke played by penguin-pirate I thought you did actually get an answer....
Quote by Pharoah
Can God create a hot dog so hot even he couldn't eat it?

Lyke omg D@ @p0OcpLpSYe.
#13
Quote by Kroach
oh **** lol I'm sorry I didn't notice the subtle joke played by penguin-pirate I thought you did actually get an answer....


Haha thank you.
Sig space for rent.
$100 obo
Message for negotiaton.
#14
Quote by mabozar

Hopefully someone can help with this linear programming question

Any Chemical Engineers / Maths guys on ?

--------------------------------------------------------------------------------

A chemical plant makes three products (E, F and G) and utilises three raw materials (A, B and C) in limited supply. Each of the three products is produced in a separate process (1, 2 and 3) as shown in the diagram.


The available materials A, B and C do not have to be totally consumed. The reactions involving A, B and C are as follows:


Process 1: A + B = E
Process 2: A + B = F
Process 3: 3A + 2B + C = G
Raw Material Maximum Available, kg/day Cost pence/kg
A 30,000 1.5
B 20,000 2.0
C 15,000 2.5


Process Product Reactant Requirements (kg) per kg product Processing Cost Selling price of product
1 E 2/3 A, 1/3 B 1.5 pence/kg E 4.5 pence/kg E
2 F 2/3 A, 1/3 B 0.5 pence/kg F 3.9 pence/kg F
3 G 1/2 A, 1/6 B, 1/3 C 1.0 pence/kg G 3.0 pence/kg G


NB. Mass is conserved

It is required to formulate this as an optimisation problem. Set up and identify:

An objective function to maximise the total operating profit per day
Equality Constraints
Inequality Constraints
You are not required to solve this problem.
Quote by saphrax
Seems easy enough to me...


lol first thing i thought of when i saw this
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#15
Anyone offer a struggling honest student a bit of direction would be much appreciated. No more posts from me so if nobody gives me some positive feedback I shall take the hint.

Cheers anyway
GLASGOW CELTIC - CHAMPIONS 2006-2007
#16
Does it involve indifference curves and the like? Does it involve optimizations and budget constraints? I study economics myself and encounter some of these problems (without the engineering parts). I could solve it for you but I don't want you to have the easy way. I want you to learn for yourself. Instead I'm gonna give some clues to make your work easier, remember I'm solving these in an economic way so it might not be entirely correct:

1. Substitute numbers to each variable given the problem to solve the equation.

2. Make a budget line. How? Get the intercepts of both X & Y. Since your equations are not that different from the simple X + Y = Z, I'm pretty sure you understand this

3. Get the indifference curves for each equation. I'm not gonna teach you how but I'm sure you've encountered this equation before X/Y = Py/Px (or was it the other way around?). Use it

4. Happy solving