711.sagews

# NO UNCERTAINTY

b, c = var('b,c')
threshold = 0

# Generate graphic objects
a_plot = region_plot(-4*b^3+c^3+3*b*c^2+(b*(b^2*(6-2*c)-c*(b+c)))/(c*(1+b-c))>=threshold, 
         (b,0,.5), (c,0,.5), plot_points=300, incol='lightblue', bordercol='black')

a_ray = implicit_plot(c-b/3==0, (b,0,.5), (c,0,.5), plot_points=300)
b_ray = implicit_plot(c-b/2==0, (b,0,.5), (c,0,.5), plot_points=300)
c_ray = implicit_plot(c-b==0, (b,0,.5), (c,0,.5), plot_points=300)

# Combine and display graphic objects
combined = (a_plot + a_ray + b_ray + c_ray)
combined.show(aspect_ratio=1)

# UNCERTAINTY WITH TWO HOTELS

b, c = var('b,c')
threshold = 0

# Generate graphic objects
a_plot = region_plot(c-2*b>=threshold, 
         (b,0,.5), (c,0,.5), plot_points=300, incol='lightblue', bordercol='black')

a_ray = implicit_plot(c-b/3==0, (b,0,.5), (c,0,.5), plot_points=300)
b_ray = implicit_plot(c-b/2==0, (b,0,.5), (c,0,.5), plot_points=300)
c_ray = implicit_plot(c-b==0, (b,0,.5), (c,0,.5), plot_points=300)

# Combine and display graphic objects
combined = (a_plot + a_ray + b_ray + c_ray)
combined.show(aspect_ratio=1)

# UNCERTAINTY WITH THREE HOTELS, LHS = 0.1

b, c = var('b,c')
threshold = 0.1

# Generate graphic objects
a_plot = region_plot((b-c)*(b^4*(4+10*c-8*b)+c^3*(8*b^2-3*b*c-2*c^2)+b^2*c*(8*c-12*b-3*b*c))/
                     (2*(2*b^2-2*b*c-c^2)^3)>=threshold, 
         (b,0,.5), (c,0,.5), plot_points=300, incol='lightblue', bordercol='black')

a_ray = implicit_plot(c-b/3==0, (b,0,.5), (c,0,.5), plot_points=300)
b_ray = implicit_plot(c-b/2==0, (b,0,.5), (c,0,.5), plot_points=300)
c_ray = implicit_plot(c-b==0, (b,0,.5), (c,0,.5), plot_points=300)

# Combine and display graphic objects
combined = (a_plot + a_ray + b_ray + c_ray)
combined.show(aspect_ratio=1)

# UNCERTAINTY WITH THREE HOTELS , LHS = 0.2

b, c = var('b,c')
threshold = 0.2

# Generate graphic objects
a_plot = region_plot((b-c)*(b^4*(4+10*c-8*b)+c^3*(8*b^2-3*b*c-2*c^2)+b^2*c*(8*c-12*b-3*b*c))/
                     (2*(2*b^2-2*b*c-c^2)^3)>=threshold, 
         (b,0,.5), (c,0,.5), plot_points=300, incol='lightblue', bordercol='black')

a_ray = implicit_plot(c-b/3==0, (b,0,.5), (c,0,.5), plot_points=300)
b_ray = implicit_plot(c-b/2==0, (b,0,.5), (c,0,.5), plot_points=300)
c_ray = implicit_plot(c-b==0, (b,0,.5), (c,0,.5), plot_points=300)

# Combine and display graphic objects
combined = (a_plot + a_ray + b_ray + c_ray)
combined.show(aspect_ratio=1)

# UNCERTAINTY WITH THREE HOTELS , LHS = 0.3

b, c = var('b,c')
threshold = 0.3

# Generate graphic objects
a_plot = region_plot((b-c)*(b^4*(4+10*c-8*b)+c^3*(8*b^2-3*b*c-2*c^2)+b^2*c*(8*c-12*b-3*b*c))/
                     (2*(2*b^2-2*b*c-c^2)^3)>=threshold, 
         (b,0,.5), (c,0,.5), plot_points=300, incol='lightblue', bordercol='black')

a_ray = implicit_plot(c-b/3==0, (b,0,.5), (c,0,.5), plot_points=300)
b_ray = implicit_plot(c-b/2==0, (b,0,.5), (c,0,.5), plot_points=300)
c_ray = implicit_plot(c-b==0, (b,0,.5), (c,0,.5), plot_points=300)

# Combine and display graphic objects
combined = (a_plot + a_ray + b_ray + c_ray)
combined.show(aspect_ratio=1)