## Main.LinearProgramming History

See additional solution options for solving [[https://apmonitor.com/pdc/index.php/Main/LinearProgramming|Linear Programming with Python]].
Changed line 97 from:
m.Obj(-profit) # maximize
to:
m.Maximize(profit)
June 21, 2020, at 04:43 AM by 136.36.211.159 -
Deleted lines 264-282:

----

(:html:)
<script type="text/javascript">
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var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

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var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
dsq.src = 'https://' + disqus_shortname + '.disqus.com/embed.js';
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</script>
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December 04, 2019, at 04:44 AM by 12.244.228.90 -

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/2dY_tRamSjY" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
(:htmlend:)
December 04, 2019, at 03:54 AM by 12.244.228.90 -
Changed lines 27-29 from:
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''
to:
A simple production planning problem is given by the use of two ingredients ''A'' and ''B'' that produce products ''1'' and ''2''. The available supply of ''A'' is 30 units and ''B'' is 44 units. For production it requires:

* 3 units of ''A'' and 8 units of ''B'' to produce Product ''1''
* 6
units of ''A'' and 4 units of ''B'' to produce Product ''2''
December 04, 2019, at 03:48 AM by 12.244.228.90 -
Changed line 43 from:
m.Obj(-profit) # maximize
to:
m.Maximize(profit) # maximize
June 01, 2019, at 02:56 PM by 45.56.3.173 -
Changed lines 25-26 from:
!! Soft Drink Production Problem (Example 2)
to:
!!!! Soft Drink Production Problem (Example 2)
Deleted lines 32-33:
----
Deleted lines 56-57:
----
Deleted lines 76-77:

----
June 01, 2019, at 02:51 PM by 45.56.3.173 -
Changed lines 86-91 from:
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.

* [[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]]

(:toggle hide mycode1 button show="Show Gekko Python Source
":)
to:
Below are the source files for generating the contour plots in GEKKO Python and APM Python.

(:toggle hide mycode1 button show="Show Gekko Python Source with Contours"
:)
Changed lines 159-164 from:
(:toggle hide mycode2 button show="Show APM Python Source":)
to:
The linear program is solved with the APM model through a web-service while the contour plot is generated with the Python package Matplotlib.

* [[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]]

(:toggle hide mycode2 button show="Show APM Python Source with Contours
":)
June 01, 2019, at 02:49 PM by 45.56.3.173 -

!!!! Python Solution

(:source lang=python:)
from gekko import GEKKO

m = GEKKO()
x1 = m.Var(lb=0,ub=5)
x2 = m.Var(lb=0,ub=4)
profit = m.Var()

m.Obj(-profit) # maximize
m.Equation(profit==100*x1 + 125*x2)
m.Equation(3*x1+6*x2<=30)
m.Equation(8*x1+4*x2<=44)

m.solve()

print ('')
print ('--- Results of the Optimization Problem ---')
print ('Product 1 (x1): ' + str(x1.value))
print ('Product 2 (x2): ' + str(x2.value))
print ('Profit: ' + str(profit.value))
(:sourceend:)

----

!!!! Contour Plot
June 01, 2019, at 02:47 PM by 45.56.3.173 -
(:toggle hide mycode1 button show="Show Gekko Python Source":)
(:div id=mycode1:)
Changed lines 66-108 from:
# Import APM Python library
try:
from APMonitor import *
except:
# Automatically install APMonitor
import pip
pip.main(['install','APMonitor'])
from APMonitor import *

# Select the server
server = 'https://byu.apmonitor.com'

# Give the application a name
app = 'production'

# Clear any previous applications by that name
apm(server,app,'clear all')

# Write the model file
fid = open('softdrink.apm','w')
fid.write('Variables \n')
fid.write('  x1 > 0 , < 5  ! Product 1 \n')
fid.write('  x2 > 0 , < 4  ! Product 2 \n')
fid.write('  profit \n')
fid.write(' \n')
fid.write('Equations \n')
fid.write('  ! profit function \n')
fid.write('  maximize profit  \n')
fid.write('  profit = 100 * x1 + 125 * x2 \n')
fid.write('  3 * x1 + 6 * x2 <= 30 \n')
fid.write('  8 * x1 + 4 * x2 <= 44        \n')
fid.close()

# Solve on APM server
solver_output = apm(server,app,'solve')

# Display solver output
print(solver_output)

# Retrieve results
sol = apm_sol(server,app)

to:
from gekko import GEKKO

m = GEKKO()
x1 = m.Var(lb=0,ub=5)
x2 = m.Var(lb=0,ub=4)
profit = m.Var()

m.Obj(-profit) # maximize
m.Equation(profit==100*x1 + 125*x2)
m.Equation(3*x1+6*x2<=30)
m.Equation(8*x1+4*x2<=44)

m.solve()

Changed lines 82-88 from:
print ('Product 1 (x1): ' + str(sol['x1']))
print ('Product 2 (x2): ' + str(sol['x2']))
print ('Profit: ' + str(sol['profit']))

# Display Results in Web Viewer
url = apm_web_var(server,app
)
to:
print ('Product 1 (x1): ' + str(x1.value))
print ('Product 2 (x2): ' + str(x2.value))
print ('Profit: ' + str(profit.value))
(:divend:)

(:toggle hide mycode2 button show="Show APM Python Source":)
(:div id=mycode2:)
(:source lang=python:)
# Import APM Python library
try:
from APMonitor import *
except:
# Automatically install APMonitor
import pip
pip.main(['install','APMonitor'])
from APMonitor import *

# Select the server
server = 'https://byu.apmonitor.com'

# Give the application a name
app = 'production'

# Clear any previous applications by that name
apm(server,app,'clear all')

# Write the model file
fid = open('softdrink.apm','w')
fid.write('Variables \n')
fid.write('  x1 > 0 , < 5  ! Product 1 \n')
fid.write('  x2 > 0 , < 4  ! Product 2 \n')
fid.write('  profit \n')
fid.write(' \n')
fid.write('Equations \n')
fid.write('  ! profit function \n')
fid.write('  maximize profit  \n')
fid.write('  profit = 100 * x1 + 125 * x2 \n')
fid.write('  3 * x1 + 6 * x2 <= 30 \n')
fid.write('  8 * x1 + 4 * x2 <= 44        \n')
fid.close()

# Solve on APM server
solver_output = apm(server,app,'solve')

# Display solver output
print(solver_output)

# Retrieve results
sol = apm_sol(server,app)

print ('')
print ('--- Results of the Optimization Problem ---')
print ('Product 1 (x1): ' + str(sol['x1']))
print ('Product 2 (x2): ' + str(sol['x2']))
print ('Profit: ' + str(sol['profit']))

# Display Results in Web Viewer
url = apm_web_var(server,app)

## Generate a contour plot
# Import some other libraries that we'll need
# matplotlib and numpy packages must also be installed
import matplotlib
import numpy as np
import matplotlib.pyplot as plt

# Design variables at mesh points
x = np.arange(-1.0, 8.0, 0.02)
y = np.arange(-1.0, 6.0, 0.02)
x1, x2 = np.meshgrid(x,y)

# Equations and Constraints
profit = 100.0 * x1 + 125.0 * x2
A_usage = 3.0 * x1 + 6.0 * x2
B_usage = 8.0 * x1 + 4.0 * x2

# Create a contour plot
plt.figure()
# Weight contours
lines = np.linspace(100.0,800.0,8)
CS = plt.contour(x1,x2,profit,lines,colors='g')
plt.clabel(CS, inline=1, fontsize=10)
# A usage < 30
CS = plt.contour(x1,x2,A_usage,[26.0, 28.0, 30.0],colors='r',linewidths=[0.5,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)
# B usage < 44
CS = plt.contour(x1, x2,B_usage,[40.0,42.0,44.0],colors='b',linewidths=[0.5,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)
# Container for 0 <= Product 1 <= 500 L
CS = plt.contour(x1, x2,x1 ,[0.0, 0.1, 4.9, 5.0],colors='k',linewidths=[4.0,1.0,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)
# Container for 0 <= Product 2 <= 400 L
CS = plt.contour(x1, x2,x2 ,[0.0, 0.1, 3.9, 4.0],colors='k',linewidths=[4.0,1.0,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)

plt.title('Soft Drink Production Problem')
plt.xlabel('Product 1 (100 L)')
plt.ylabel('Product 2 (100 L)')
# Save the figure as a PNG
plt.savefig('contour.png')

# Show the plots
plt.show()
(:sourceend:)
(:divend:)

(:source lang=python:)
# Import APM Python library
try:
from APMonitor import *
except:
# Automatically install APMonitor
import pip
pip.main(['install','APMonitor'])
from APMonitor import *

# Select the server
server = 'https://byu.apmonitor.com'

# Give the application a name
app = 'production'

# Clear any previous applications by that name
apm(server,app,'clear all')

# Write the model file
fid = open('softdrink.apm','w')
fid.write('Variables \n')
fid.write('  x1 > 0 , < 5  ! Product 1 \n')
fid.write('  x2 > 0 , < 4  ! Product 2 \n')
fid.write('  profit \n')
fid.write(' \n')
fid.write('Equations \n')
fid.write('  ! profit function \n')
fid.write('  maximize profit  \n')
fid.write('  profit = 100 * x1 + 125 * x2 \n')
fid.write('  3 * x1 + 6 * x2 <= 30 \n')
fid.write('  8 * x1 + 4 * x2 <= 44        \n')
fid.close()

# Solve on APM server
solver_output = apm(server,app,'solve')

# Display solver output
print(solver_output)

# Retrieve results
sol = apm_sol(server,app)

print ('')
print ('--- Results of the Optimization Problem ---')
print ('Product 1 (x1): ' + str(sol['x1']))
print ('Product 2 (x2): ' + str(sol['x2']))
print ('Profit: ' + str(sol['profit']))

# Display Results in Web Viewer
url = apm_web_var(server,app)

## Generate a contour plot
# Import some other libraries that we'll need
# matplotlib and numpy packages must also be installed
import matplotlib
import numpy as np
import matplotlib.pyplot as plt

# Design variables at mesh points
x = np.arange(-1.0, 8.0, 0.02)
y = np.arange(-1.0, 6.0, 0.02)
x1, x2 = np.meshgrid(x,y)

# Equations and Constraints
profit = 100.0 * x1 + 125.0 * x2
A_usage = 3.0 * x1 + 6.0 * x2
B_usage = 8.0 * x1 + 4.0 * x2

# Create a contour plot
plt.figure()
# Weight contours
lines = np.linspace(100.0,800.0,8)
CS = plt.contour(x1,x2,profit,lines,colors='g')
plt.clabel(CS, inline=1, fontsize=10)
# A usage < 30
CS = plt.contour(x1,x2,A_usage,[26.0, 28.0, 30.0],colors='r',linewidths=[0.5,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)
# B usage < 44
CS = plt.contour(x1, x2,B_usage,[40.0,42.0,44.0],colors='b',linewidths=[0.5,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)
# Container for 0 <= Product 1 <= 500 L
CS = plt.contour(x1, x2,x1 ,[0.0, 0.1, 4.9, 5.0],colors='k',linewidths=[4.0,1.0,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)
# Container for 0 <= Product 2 <= 400 L
CS = plt.contour(x1, x2,x2 ,[0.0, 0.1, 3.9, 4.0],colors='k',linewidths=[4.0,1.0,1.0,4.0])
plt.clabel(CS, inline=1, fontsize=10)

plt.title('Soft Drink Production Problem')
plt.xlabel('Product 1 (100 L)')
plt.ylabel('Product 2 (100 L)')
# Save the figure as a PNG
plt.savefig('contour.png')

# Show the plots
plt.show()
(:sourceend:)
January 27, 2014, at 03:59 AM by 23.255.228.67 -
Changed line 20 from:
<iframe width="560" height="315" src="//www.youtube.com/embed/i8WS6HlE8qM?list=UU2GuY-AxnNxIJFAVfEW0QFA" frameborder="0" allowfullscreen></iframe>
to:
<iframe width="560" height="315" src="//www.youtube.com/embed/i8WS6HlE8qM" frameborder="0" allowfullscreen></iframe>
January 27, 2014, at 03:58 AM by 23.255.228.67 -
!!!! Refinery Optimization with Linear Programming
Changed lines 10-11 from:
* [[https://apmonitor.com/online/view_pass.php?f=irefinery.apm | Solve Refinery Optimization Problem]] with Integer Variables
to:
(:htmlend:)

!!!! Refinery Optimization with Mixed Integer Linear Programming

* [[https://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>
January 23, 2014, at 03:01 PM by 23.255.228.67 -
Deleted lines 4-5:
!!!! Linear Programming Example 1
Changed lines 14-15 from:
!!!! Linear Programming Example 2
to:
----

!! Soft Drink Production Problem (Example 2)
Deleted lines 28-29:
----
Deleted lines 35-36:

----
January 23, 2014, at 03:00 PM by 23.255.228.67 -
Changed lines 5-16 from:
!!!! Linear Programming Example
to:
!!!! 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.

* [[https://apmonitor.com/online/view_pass.php?f=refinery.apm | Solve Refinery Optimization Problem]] with Continuous Variables
* [[https://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
February 18, 2013, at 10:53 PM by 69.169.188.188 -
Deleted line 15:
February 18, 2013, at 10:52 PM by 69.169.188.188 -
Changed line 46 from:
* [[Attach:linear_programming_with_apm_python.zip|Attach:linear_programming_with_apm_python.png]]
to:
[[Attach:linear_programming_with_apm_python.zip|Attach:linear_programming_with_apm_python.png]]
February 18, 2013, at 10:49 PM by 69.169.188.188 -
Changed line 26 from:
to:
Changed line 36 from:
to:
February 18, 2013, at 10:49 PM by 69.169.188.188 -
Changed line 26 from:
to:
Changed line 36 from:
to:
February 18, 2013, at 10:49 PM by 69.169.188.188 -
Changed lines 21-25 from:
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.

* [[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]]
to:
!!!! Soft Drink Production Problem

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

(:html:)
...</iframe>
(:htmlend:
)

----

!!!! Modified Production Problem

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

(
:html:)
<iframe src="https://apmonitor
(:htmlend:)

----

!!!! 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.
February 18, 2013, at 09:21 PM by 69.169.188.188 -
Changed lines 8-12 from:
* 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.

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.

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

----

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.
February 18, 2013, at 09:00 PM by 69.169.188.188 -
(: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]]

----

(:html:)
<script type="text/javascript">
/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */
var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

/* * * DON'T EDIT BELOW THIS LINE * * */
(function() {
var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
dsq.src = 'https://' + disqus_shortname + '.disqus.com/embed.js';