[#07] Manual do Lingo - Preço sombra - YouTube

Hello! How are you?

Let's continue our Lingo's manual video series

We entered here starting with Lingo

Examining solution and dual price reports

So,

we have here our model when we solve

we have dual price information in relation to our mathematical equations

Here are the lines, so we have the first

which is precisely the objective function

and then our three restrictions

And we have the value here of the dual price of 25, 0 and 75

So what is the interpretation

can we have this value of 25 here?

If we can increase

in 1 the right value of this constraint

ie here where we have the value of 100

Ergo go from 100 to 101 ...

we will have an increase in our objective function of

25 units, and what i'm saying is that

if we increase here from the standard now 101

our objective function goes to value

to 14.525

Let's do the test here, I'll change to 101

I'll solve it and look here the

the function, look at the value of our objective function

14.525. Then I'll come back here

to the previous one. I will solve again

And here we have the value of zero. Why do we have this value of zero?

Because in this equation we already have

a break of 90 computers, so ...

I already have computers

Here from this restriction, that I could

build the most. Because?

Why we only produce 30 turbo computers

So we have a slack of 90

So if I increased one unit here

I would have 91 computers without using

Note that in both

equations i have a positive value here

of our restrictions, I just don't have

no slack or surplus, so ...

I'm on the edge of these restrictions

of the 100 computers I've used the 100

here, from 160 hours I already used the

160

So, in this one, that I have a break

Putting one more unit won't bring me any

benefit

And finally we have here the last restriction, that she ...

there's no slack, so there's a

dual price ... of 75

So if I increase here to 171

Our objective function goes to the value of 14.575

Let's do the simulation here

I'll change it to 171 for us to check. I will solve

And note that our value went to

14.575

Then I will come back here again to the previous

And what interpretation can we have then

of these values. Why is there such a price? The name of

dual price here also called shadow price

It's called the shadow price, precisely because

this is the value you

the maximum amount you can afford

if you want to increase this unit. For example...

If you want to increase by one hour, the journey

workforce, ie to increase by 160

for 161 hours, it will be worth it as long as

the cost you have to do that

be less than 75 units

For example, if to increase by 1 hour, you have the cost

of 60 units, it will be worth it. Why?

Because you will have a cost of 60 but you

will increase your profit

In...

for sale, at 75, ergo ...

60 minus 75

you will have a final profit of 15

Now if to increase 1 hour you will have a cost of

100

units, then it's not worth it because you just

would win 75

So 75 minus 100

would you be at a loss of 25

As well as the reduced cost

the shadow price also has the range in which it operates

we will see this a little further on, but to activate it

we have to come here in solver, options

general solver, and here where there are dual contations

we have to mark price and range

After we mark this ...

After we solve the model and after you solve the model, you can

come here in the solver and click on range

and it tells you, what is the range that those values

gives...

from ... so much from ...

reduced cost how much of the shadow price are

valid, but this we will see a little later

I recommend you leave this deactivated by default, because

it spends an extra computational time getting

in these values, so only activate when you are going to

use

Well, then we understand what dual price is and why

that he is called shadow price

The value this objective function will increase

when you increase by one unit the right side of the

your equation

Then our objective function has the value right there of 1

Why when we increase by 1

our objective function, it increases by 1

It's kind of obvious

If your objective function increases by 1

Its objective function increases by 1 unit, so

for each unit you increase in your objective function it will increase

also a unit, so it has here the value of 1

and for the other restrictions you will have

the value that Lingo will solve for you

Well, other videos like this you can find here on the channel and

on the site sudocontrol.com.br

Don't forget to leave your tips and suggestions for upcoming videos.

Here in the comments. I'll meet you soon,

See you!