# MSPA 400 Session #3 Python Module #3

# Reading assignment: Investigate the Canopy Doc Manager. Review the portion

# dealing with Matplolib. Review the gallery and the code used.

# Module #3 objectives: 1) plot inequalities, 2) show feasible regions, and

# 3) solve a linear programming problem.

import matplotlib.pyplot

from matplotlib.pyplot import *

import numpy

from numpy import *

# This is a minimization problem. One objective is to demonstrate plotting an

# unbounded region. There are four inequalities: x+3y >= 15, 3x+y >= 10,

# x >= 0, y >= 0. One inequality and the objective function have been

# modified for this module. The objective function is z = 2x+3y. The feasible

# region will be graphed and filled. Matrix methods will be used to evaluate

# the objective function at each corner.

x= arange(0,20.1,0.1)

y0= arange(0,20.1,0.1)

y1= 10.0-3.0*x

y2= 5.0-x/3.0

# The definition of y3 will allow filling the unbounded region in the plot.

y3= 20+0.0*x

# The filling will be between y3 and the maximum of y1 and y2. Need to define

# a new array y4 which will be that maximum.

y4=[0]*len(x)

for k in range(0,len(x)):

if y1[k] >= y2[k]:

y4[k]=y1[k]

if y2[k] > y1[k]:

y4[k]=y2[k]

# This is the objective function plotted for illustration.

y5= 5.5-2.0*x/3.0

# Plot limits must be set for the graph.

xlim(0,20)

ylim(0,20)

# Plot axes need to be labled,title specified and legend shown.

xlabel('x-axis')

ylabel('y-axis')

title('Shaded Area Shows the Feasible Region')

plot(x,y2,color='b')

plot(x,y1,color='r')

# This next step shows how to plot a line using different symbols.

plot(x,y5,'k--')

print ('Note that the dashed line passes through the optimum point')

# The order of entry of labels in the plt.legend statement must follow

# the order of the plt.plot statements to match colors.

legend(['x+3y >= 15','3x+y >= 10', '16.5 = 2x+3y'], 'best')

fill_between(x,y3,y4, color='grey',alpha=0.2)

show()

# Corner points for evaluation using the objective function.

x= [0, 1.5, 15]

y= [10, 4.5, 0]

# This next step shows how to use matrix calculations to evaluate

# the objective function at each corner point and find the maximum.

obj= matrix([2.0,3.0])

obj= transpose(obj)

corners= matrix([x,y])

corners= transpose(corners)

result= dot(corners,obj)

print ('Value of Objective Function at Each Corner Point\n'), result

# Exercise: Using the matrix methods shown above, verify the calculations

# in Lial Section 4.3 Example 1. Compare your code to the answer sheet.