# Using LINDO to Solve a Linear Programming Problem

I want to know how to use Lindo to solve an example in my textbook. Please need detail instructions so I can feel comfortable using LINDO to solving larger problems, The example in the text uses excel spreadsheet, but I want to know how to use LINDO without excel.

How do I write out the objective function, supply and demand constraints and how do I use LINDO, step by step to find minimum cost production plan that meet the demand of each product within the given time limit of each plant? How do I write out the dual out? Describe the economic interpretation for dual problem. Would the mmgt save $ by increasing capacity for city 1 and city 3? Is it benefial to increase the capacity for city 4 by paying $5.00 for each hr. Is it bendfical to increase the capacity for city 2 by paying $10.00 for each hr. I need to see how each part is written out and how do I use LINDO to solve.

Please see attached document

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#### Solution Preview

City 1 City 2 City 3 City 4 Demand?

Cost Hrs Cost Hrs. Cost Hrs Cost Hrs ?

Plant 1 20 0,1 30 0,2 40 0,3 50 0,4 35?

Plant 2 30 0,2 40 0,3 50 0,4 60 0,5 50?

Plant 3 40 0,3 50 0,4 60 0,5 70 0,6 40?

Supply 45 20 30 30 ?

MIN 20 x11+30 x12+ 40 x13+ 30 x21+ 40 x22+ 50 x23+ 4 x31+ 50 x32+ 60 x33+ 50 x41 + 60 x42 + 70 x43

SUBJECT TO

0.1 x11+0.2 x12+ 0.3 x13<=45

0.2 x21+ 0.3 x22+ 0.4 x23<=20

0.3 x31+ 0.4 x32+ 0.5 x33<=30

0.4 x41 +0.5 x42 + 0.6 x43<=30

x11+x21+x31+x41>=35

x12+x22+x32+x42>=50

x13+x23+x33+x43>=35

END

Dear my friend

Thank you so much for choosing our group to get service. We hope that you will be satisfied about what you need.

We would be so happy if we could help you and your friends. We try to help you in such a way that you could be able to continue and be less independent to some one else.

I tried to answer you in such a way that you can continue to working with Lindo easily.

If I could underestood your model it can be modeled as follow in Lindo

Lindo is very simple application. you write the model like what you write in paper.

%%%%%%%%%%%%%

! Xij the amount of demand from city i which is supplied by plant j

MIN 20 x11+30 x12+ 40 x13+ 30 x21+ 40 x22+ 50 x23+ 4 x31+ 50 x32+ 60 x33+ 50 x41 + 60 x42 + 70 x43

SUBJECT TO

0.1 x11+0.2 x12+ 0.3 x13<=45

0.2 x21+ 0.3 x22+ 0.4 x23<=20

0.3 x31+ 0.4 x32+ 0.5 x33<=30

0.4 x41 +0.5 x42 + 0.6 x43<=30

x11+x21+x31+x41>=35

x12+x22+x32+x42>=50

x13+x23+x33+x43>=35

END

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as you can see it is easily readable and there is no need to describe it more.

So when you copy the text between %%%%% and %%% in a file with extension LTX then you can load an run it in Lindo.

after solving that Lido will ask you that if you want that sensivity analysis done do it. You will ask it to do it and then you will have a full describtion of what you are looking for.

Abou the dual : The value of the dual variable can be seen there and you can find them . Whcih you can see from below.

LP OPTIMUM FOUND AT STEP 7

OBJECTIVE FUNCTION VALUE

1) 2200.000

VARIABLE VALUE REDUCED COST

XMON 2.000000 0.000000

XTUE 2.000000 0.000000

XWED 4.000000 0.000000

XTHU 3.000000 0.000000

XFRI 3.000000 ...

#### Solution Summary

LINDO is used to Solve a Linear Programming Problem. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.