Orchid Wedding Cakes 2010

Optimization

Problem:

"The mayor of San Nico will get in our town the president of Mexico in the town square, for which the area must be present for that day, say that the remaining days for its arrival is 3, then the mayor wants to find the most optimal way to leave the area very well presented by that date "

Suppose that the mayor has a budget of $ 1,166,666.6 for a week so the for 3 days are $ 500,000, which is derived from taxes paid by citizens, and to fix issues in the area are:

1.

Garbage

2.

Painting

3.Mantenimiento

The site area is 1800m to square grooming:

The mayor has 3 companies that are in charge of the work required and are as follows;

Option 1:

They take 5 days to do this work and charge a 150 % more for each day less to postpone the date. The weight of what they charge for each aspect is:

1. Garbage → $ 25 C/m2
2. Painting C/m2 → $ 100 → $ 80
3.Mantenimiento C/m2

f (x) = ((25x +100 x +80 x) • 3) + z

if z = 25x +100 x +80 x

Option 2

They fit the limit of time the client needs to work. The weight of what they charge for each aspect is:

1. Garbage → $ 35 C/m2
2. Painting → $ 90 C/m2
3. Maintenance → $ 50 C/m2

f (x) = 35x +90 x +50 x

Option 3

They tered 2 days to do its job and make a 5% discount for each day of term you leave it more.

1. Garbage → $ 60 C/m2
2. Painting → $ 110c/m2
3. Maintenance → $ 70 C/m2

f (x) = 60x +110 x +70 x - (z (0.05))

if z = 60x +110 x +70 x

What will be the most optimal way to order the job?

As the area = 1800m2 then the costs of each of the companies are:

Option 1 1. Garbage → $ 202.500
2. → Painting → 3.Mantenimiento
$ 810.000 $ 144.000

= $ 1,156,500 + 300%
Total = $ 4,626,000

Option 2 1. Garbage → $ 63.500
2. → Painting → 3.Mantenimiento
$ 162.000 $ 90.000

Total = $ 169.200

Option 3

1. Garbage → $ 108.000
2. Painting → $ 198.000
3.Mantenimiento → $ 126.000

= $ 432.000 - 5%
Total = $ 410.400

asymptotic complexity

the most optimal way would be to find a lower bound to the budget , but the more remote this is less the cost will, therefore, more optimal.

In this case, as shown in the graph the optimal height to choose option 2 is blue, and that meets the requirements to optimize the work, is below the altitude of income (green) and is also the lowest level, therefore the least expensive.

This decision problem belongs to the class "P", since the choice is not very complicated and the equations of each option are linear, that is why it is very difficult to resolve. Apart
these algorithms do not belong to an NP-hard problem, because for start as it is a NP problem can not therefore be NP-hard.

This is a representation of the algorithm:

* This is not a flow chart is a representation only simple diagram of the algorithm.



References:

http://www.google.com.mx/
http://es.wikipedia.org/wiki/NP-hard
http:// es.wikipedia.org / wiki / Clases_de_complejidad_P_y_NP
http://es.wikipedia.org/wiki/Cota_superior_asint% C3% B3tica
http://es.wikipedia.org/wiki/Optimizaci% C3% B3n_de_software
http://maps.google.com.mx/?gclid=CKvjnPWen6ACFSpeagodMlwzag
http://es.wikipedia.org/wiki/Problema_de_decisi% C3% B3n