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#1 2014-10-14 00:09:49

Anson
Guest

Urgent - Linear Programming

ChemCo is producing a chemical product in three different grades; Grade I (lowest quality), Grade II (medium quality) and Grade III (highest quality). The company buy a raw material at the cost of $6 per 100 litres. At the additional cost of $3 and the usage of 3 hours of process time, 100 litres of raw material produce 60 litres of Grade I and 40 litres of Grade II. The Grade II product can be sold as it is or processed further. At the extra cost of $1 and 1 more hour of process time, 100 litres of Grade II can produce 60 litres of Grade III and 40 litres of Grade I. The price and the maximum demand of each grade are given in the following table.

Grade I
price: $12 / litre
maximum demand: 60 litre / day
Grade II
price: $16 / litre
maximum demand: 40 litre / day
Grade III
Price: $26 / litre
Maximum Demand: 30 litres/day

The company has the capacity of 5 hours of process time per day. Develop a LP formulation for ChemCo to maximise their daily profit. Also, use suitable computer software to solve the LP problem. Since those are chemical products, assume no overproduction is allowed (i.e. you cannot produce more than its maximum demand). Write concisely any further assumptions you made in the formulation.

#2 2014-10-14 03:42:24

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Urgent - Linear Programming

hi Anson,

So have you managed to get any of the constraint equations ?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2014-10-14 03:48:48

anson
Member
Registered: 2014-10-14
Posts: 2

Re: Urgent - Linear Programming

I have not managed to obtain the constraint.

anson

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#4 2014-10-14 21:06:36

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Urgent - Linear Programming

hi anson,

When there's a lot of text like this, I like to summarise the key information in a table.  Here's mine:

VlSOzgX.gif

Initially I thought there would be three variables, x y and z, for the three grades.  But as I created the table, I realised that there are only two choices: how much raw material is given the stage one processing, and then how much of the resulting grade 2 is given the stage two processing.  So that fixes just two variables, so I've used x for the first stage processing and y for the second.

So let's say that x is the amount of raw material that is given the first stage process to convert it into grade 1 and grade 2 product.  I'll measure x in 100s of litres.

And y is the amount of grade 2 that is given the second stage process to convert it into grade 3 and grade 1 product.  I'll measure y in 100s of litres.

So let's now make a model for the stage one process.  I'll take x of raw and convert it:

cost = 6x + 3x
time = 3x
grade 1 produced = ????
grade 2 produced = 0.4x

Now let's model the stage two process.  I'll take y of the grade 2 and convert it:

cost = y
time = ???
grade 1 produced = 0.4y
grade 3 produced = 0.6y

And the final amounts are now:

grade 1 = ???? + 0.4y
grade 2 = 0.4x - y
grade 3 = ????

total time = 3x + y

total cost = 9x + y

total sale value = ????

I've left a few ??? so you get to put in some of the answers yourself.

One constraint will be that y cannot be bigger than the amount of grade 2 available.  ie.  y ≤ 0.4x

There will be a time constraint and three constraints due to the maximum amounts that can be made.

The profit will be sales - costs. 

Is that enough for you to complete this?

Please post back with your progress.  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2014-10-14 22:40:34

anson
Member
Registered: 2014-10-14
Posts: 2

Re: Urgent - Linear Programming

Hi Bob,

I have managed to determine the ???. however, I could obtain the equation and constraint to be enter into my software "Management Scientist" to generate the output solution.

Regards,
Anson

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#6 2014-10-15 05:23:30

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Urgent - Linear Programming

hi anson,

I see you have become a member.  Welcome.  smile

I suggest you copy my post and re-post it back with your answers to the ???.  Then I can see if you are doing it correctly.

I've not used Management Scientist but I looked it up and it should handle this problem.  Have you managed to use it for a simpler linear programming problem?

If yes, then please post that one and your solution.  Thanks.

What I am trying to find out  is "What can you do already"?  So far I am unclear about this.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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