Math Is Fun Forum

austin81

Member

Registered: 2005-03-21

Posts: 39

Linear Programming

Please LI'll like to know the meaninings of these terms as applied in Linear Programming:
Objective function, Contraints, feasible solution, feasible  region, optimal solution, raetest and Least values.
Thanks

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: Linear Programming

This should be of some help.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

austin81

Member

Registered: 2005-03-21

Posts: 39

Re: Linear Programming

Thanks ery much> I just discovered there's more in Linear Programming than I thought of.

336337

Guest

Re: Linear Programming

I can't put this problem into a model. I hope that there is someone who has some time for me.

Company X produces the product A. Before A is finished, there're 3 processus. Proces 1, from the raw material to an intermediate product B. Proces 2, from intermdiate B to intermediate product C. And proces 3, from intermediate C to the final product A.
The maximum demand for product A in the next 4 weeks is:
week 1: 375
week 2: 570
week 3: 750
week 4: 480
Product A is sold at 350/unit
Company X can employ their labourers on a weekly contract at 250/week. Each labourer works 40 hours.
It takes 0.5 hour for a labourer to complete process 1 for 1 unit, 1 hour to complete process 2 for 1 unit, and 0.25 hour to complete process 3.
The company can employ maximum 12 people. And a labourer needs to do the same process a whole week, so it can't work on process one on monday and the next day continue with process 2.
The intermediate and final products can aslo be stored, the cost for storage is 40 a week for product A, 15 a week for product B and 20 a weel for product C. At the end of week 4 all storage must be sold.

I need to maximise the profit but I can't find it. It would be great if someone could help me.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Linear Programming

I'm not impressed that the laborers can't switch places each day because constraints
employers put like that simply induce things like carpal tunnel and other
repetitive injuries.  Variety is a good thing.

---

igloo myrtilles fourmis

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Linear Programming

The question isn't so hard but there are a lot of things to consider.

---

IPBLE:  Increasing Performance By Lowering Expectations.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Linear Programming

I love your festive avatar, krazzi!

This question looks like it needs decision maths, which I don't do. I have a textbook lying around though, so if no one else manages to do this then I'll teach myself how to do this type of problem and then solve yours for you.

---

Why did the vector cross the road?
It wanted to be normal.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Linear Programming

I am seeing my avatar whitout any hat!
I can't understand the problem at all. But i'll try:
So if x is number of workers that are working only I process, y-second, z-third, then
x+y+z<=12
For 4 weeks thet must be producted equal mass from all the products,so
4(40.0,5.x)=4(40.1.y)=4(40.0,25.z)
∴
x=2z
y=4z

But x,y and z are natural, so 7z<=12; and z should be 1.
Hm, interesting. Here we don't have to use operational theory.
Is my answer correct?
{2,4,1}

---

IPBLE:  Increasing Performance By Lowering Expectations.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Linear Programming

No ,sorry. I haven't saw that we can sell every week.

---

IPBLE:  Increasing Performance By Lowering Expectations.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Linear Programming

Cost of raw material ordering quantities is missing from the given data.
Assume if we maximize # units sold, we maximize profit, since we aren't
given raw material price or other overhead costs.  Storage costs is not
specified if it is per unit or for all of each type.  Also I am assuming
that no B's or C's are made, so you have to wait 1.5 hours before the
last step can be started in week 1, so this affects week 1 a little.
The results are guesswork below;I have no equations or methods:
WEEK 1:
making B 4men  160/.5=320units
making C 7men  312/1=312units
making A 1men  38.5/.25=154units
week 1 sold 154, 8 B's left, 158 C's left
WEEK 2:
making B 4men  320made + 8 units leftover = 328 units
making C 6men  240made + 158 units leftover = 398 units
making A 2men  320 units
week 2 sold 320, 88 B's left, 78 C's left
WEEK 3:
making B 4men  320made + 88 units leftover = 408 units
making C 6men  240made + 78 units leftover = 320 units
making A 2men  320 units
week 3 sold 320, 168 B's left, 0 C's left
WEEK 4: (ten workers on last week)
making B 1man 80made + 168 leftover = 248 units
making C 7men 248made with some wasted time
making A 2men 248made with much wasted time
week 4 sold 248, no product left over.
This analysis was just guesswork, so it's better than nothing.
Hope it helps.

---

igloo myrtilles fourmis