#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
#
#-----

save_plots = F

# Chapter 7: Section 7: Exercise 8
#

# Plot the feasible region for the primal problem:
# 
x = seq( from=-1, to=50, length.out=100 )
y = 20 - x

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_7_prob_8_primal_region.eps", onefile=FALSE, horizontal=FALSE) }

plot( x, y, type='l', xlim=c(-1,+60), ylim=c(-1,30), xlab='x_1', ylab='x_2' ) 

y = ( -50 + x )/ (-2) 
lines( x, y, type='l', col='blue' )

abline( h=0 )
abline( v=0 ) 

polygon( c(0,20,0), c(0,0,20), col='gray' )
polygon( c(50,70,70,0,0), c(0,0,40,40,25), col='gray' )

grid()

if( save_plots ){ dev.off() }


# Plot the feasible region for the dual problem:
#
x = seq( from=-1, to=10, length.out=100 )
y = x - 2 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_7_prob_8_dual_region.eps", onefile=FALSE, horizontal=FALSE) }

plot( x, y, type='l', xlim=c(-1,+10), ylim=c(-1,10), xlab='v_1', ylab='v_2' ) 

y = (x - 1)/2
lines( x, y, type='l', col='blue' )

abline( h=0 )
abline( v=0 ) 

x_inf = 15
y_inf = ( x_inf - 1 ) / 2 
polygon( c(2,x_inf,x_inf,3,2), c(0,0,y_inf,1,0), col='gray' )

grid()

if( save_plots ){ dev.off() }