## Main.LinearProgramming History

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<iframe width="560" height="315" src="//www.youtube.com/embed/i8WS6HlE8qM~~?list=UU2GuY-AxnNxIJFAVfEW0QFA~~" frameborder="0" allowfullscreen></iframe>

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<iframe width="560" height="315" src="//www.youtube.com/embed/i8WS6HlE8qM" frameborder="0" allowfullscreen></iframe>

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!!!! Refinery Optimization with Linear Programming

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!!!! Refinery Optimization with Mixed Integer Linear Programming

* [[http://apmonitor.com/online/view_pass.php?f=irefinery.apm | Solve Refinery Optimization Problem]] with Integer Variables

(:html:)

<iframe width="560" height="315" src="//www.youtube.com/embed/i8WS6HlE8qM?list=UU2GuY-AxnNxIJFAVfEW0QFA" frameborder="0" allowfullscreen></iframe>

!!!! Refinery Optimization with Mixed Integer Linear Programming

* [[http://apmonitor.com/online/view_pass.php?f=irefinery.apm | Solve Refinery Optimization Problem]] with Integer Variables

(:html:)

<iframe width="560" height="315" src="//www.youtube.com/embed/i8WS6HlE8qM?list=UU2GuY-AxnNxIJFAVfEW0QFA" frameborder="0" allowfullscreen></iframe>

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!!~~!! Linear Programming Example~~ 2

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!! Soft Drink Production Problem (Example 2)

!! Soft Drink Production Problem (Example 2)

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!!!! Linear Programming ~~Example~~

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!!!! Linear Programming Example 1

A refinery must produce 100 gallons of gasoline and 160 gallons of diesel to meet customer demands. The refinery would like to minimize the cost of crude and two crude options exist. The less expensive crude costs $80 USD per barrel while a more expensive crude costs $95 USD per barrel. Each barrel of the less expensive crude produces 10 gallons of gasoline and 20 gallons of diesel. Each barrel of the more expensive crude produces 15 gallons of both gasoline and diesel. Find the number of barrels of each crude that will minimize the refinery cost while satisfying the customer demands.

* [[http://apmonitor.com/online/view_pass.php?f=refinery.apm | Solve Refinery Optimization Problem]] with Continuous Variables

* [[http://apmonitor.com/online/view_pass.php?f=irefinery.apm | Solve Refinery Optimization Problem]] with Integer Variables

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<iframe width="560" height="315" src="//www.youtube.com/embed/M_mpRrGKKMo?rel=0" frameborder="0" allowfullscreen></iframe>

(:htmlend:)

!!!! Linear Programming Example 2

A refinery must produce 100 gallons of gasoline and 160 gallons of diesel to meet customer demands. The refinery would like to minimize the cost of crude and two crude options exist. The less expensive crude costs $80 USD per barrel while a more expensive crude costs $95 USD per barrel. Each barrel of the less expensive crude produces 10 gallons of gasoline and 20 gallons of diesel. Each barrel of the more expensive crude produces 15 gallons of both gasoline and diesel. Find the number of barrels of each crude that will minimize the refinery cost while satisfying the customer demands.

* [[http://apmonitor.com/online/view_pass.php?f=refinery.apm | Solve Refinery Optimization Problem]] with Continuous Variables

* [[http://apmonitor.com/online/view_pass.php?f=irefinery.apm | Solve Refinery Optimization Problem]] with Integer Variables

(:html:)

<iframe width="560" height="315" src="//www.youtube.com/embed/M_mpRrGKKMo?rel=0" frameborder="0" allowfullscreen></iframe>

(:htmlend:)

!!!! Linear Programming Example 2

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[[Attach:linear_programming_with_apm_python.zip|Attach:linear_programming_with_apm_python.png]]

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink.htm" width="500" height="~~200~~" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink.htm" width="500" height="230" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink2.htm" width="500" height="~~200~~" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink2.htm" width="500" height="230" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink.htm" width="500" height="~~600~~" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink.htm" width="500" height="200" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink2.htm" width="500" height="~~600~~" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink2.htm" width="500" height="200" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

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* [[Attach:linear_programming_with_apm_python

*

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!!!! Soft Drink Production Problem

[[http://apmonitor.com/online/view_pass.php?f=softdrink.apm | Solve the Production Problem Online]]

(:html:)

<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink.htm" width="500" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

(:htmlend:)

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!!!! Modified Production Problem

[[http://apmonitor.com/online/view_pass.php?f=softdrink2.apm | Solve the Modified Production Problem Online]]

(:html:)

<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink2.htm" width="500" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

(:htmlend:)

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!!!! Solution and Contour Plots with Python

Below are the source files for generating the contour plots in Python. The linear program is solved with the APM model through a web-service while the contour plot is generated with the Python package Matplotlib.

[[http://apmonitor.com/online/view_pass.php?f=softdrink.apm | Solve the Production Problem Online]]

(:html:)

<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink.htm" width="500" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

(:htmlend:)

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!!!! Modified Production Problem

[[http://apmonitor.com/online/view_pass.php?f=softdrink2.apm | Solve the Modified Production Problem Online]]

(:html:)

<iframe src="http://apmonitor.com/me575/uploads/Main/softdrink2.htm" width="500" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>

(:htmlend:)

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!!!! Solution and Contour Plots with Python

Below are the source files for generating the contour plots in Python. The linear program is solved with the APM model through a web-service while the contour plot is generated with the Python package Matplotlib.

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* 3 units of ''A'' and 6 units of ''B'' to produce ~~product~~ ''1''

* 8 units of ''A'' and 4 units of ''B'' to produce~~product~~ ''2''

There are at most 5 units of~~product~~ 1 and 4 units of ~~product~~ 2. Product 1 can be sold for 100 and Product 2 can be sold for 125. The objective is to maximize the profit for this production problem.

* 8 units of ''A'' and 4 units of ''B'' to produce

There are at most 5 units of

to:

* 3 units of ''A'' and 6 units of ''B'' to produce Product ''1''

* 8 units of ''A'' and 4 units of ''B'' to produce Product ''2''

There are at most 5 units of Product ''1'' and 4 units of Product ''2''. Product 1 can be sold for 100 and Product 2 can be sold for 125. The objective is to maximize the profit for this production problem.

* 8 units of ''A'' and 4 units of ''B'' to produce Product ''2''

There are at most 5 units of Product ''1'' and 4 units of Product ''2''. Product 1 can be sold for 100 and Product 2 can be sold for 125. The objective is to maximize the profit for this production problem.

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A contour plot can be used to explore the optimal solution. In this case, the black lines indicate the upper and lower bounds on the production of ''1'' and ''2''. In this case, the production of ''1'' must be greater than 0 but less than 5. The production of ''2'' must be greater than 0 but less than 4.

Attach:linear_programming_contour.png

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Below are the source files for generating the contour plots in Python. The linear program is solved with the APM model through a web-service while the contour plot is generated with Matplotlib.

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(:title Linear Programming Example:)

(:keywords linear programming, mathematical modeling, nonlinear, optimization, engineering optimization, university course:)

(:description Tutorial on linear programming solve parallel computing optimization applications.:)

!!!! Linear Programming Example

A simple production planning problem is given by the use of two ingredients ''A'' and ''B'' that produce products ''1'' and ''2''. In this case, it requires:

* 3 units of ''A'' and 6 units of ''B'' to produce product ''1''

* 8 units of ''A'' and 4 units of ''B'' to produce product ''2''

There are at most 5 units of product 1 and 4 units of product 2. Product 1 can be sold for 100 and Product 2 can be sold for 125. The objective is to maximize the profit for this production problem.

----

* [[Attach:linear_programming_with_apm_python.zip|Linear Programming Example Files for APM Python (.zip)]]

* [[Attach:linear_programming_with_apm_python.zip|Attach:linear_programming_with_apm_python.png]]

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(:keywords linear programming, mathematical modeling, nonlinear, optimization, engineering optimization, university course:)

(:description Tutorial on linear programming solve parallel computing optimization applications.:)

!!!! Linear Programming Example

A simple production planning problem is given by the use of two ingredients ''A'' and ''B'' that produce products ''1'' and ''2''. In this case, it requires:

* 3 units of ''A'' and 6 units of ''B'' to produce product ''1''

* 8 units of ''A'' and 4 units of ''B'' to produce product ''2''

There are at most 5 units of product 1 and 4 units of product 2. Product 1 can be sold for 100 and Product 2 can be sold for 125. The objective is to maximize the profit for this production problem.

----

* [[Attach:linear_programming_with_apm_python.zip|Linear Programming Example Files for APM Python (.zip)]]

* [[Attach:linear_programming_with_apm_python.zip|Attach:linear_programming_with_apm_python.png]]

----

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