import gpkit
import gpkit.interactive

# transporting gravel across a river:
#   how large of a box should be used / how many trips should be taken?

V1 = gpkit.Variable("V_1", 400, "cubic yards", "volume of gravel to transport")

l = gpkit.Variable("l", "yards", "box length")
w = gpkit.Variable("w", "yards", "box width")
h = gpkit.Variable("h", "yards", "box height")

c_sides = gpkit.Variable("c_{sides}", 10, "1/yard^2", "cost of box sides and bottom")
c_ends = gpkit.Variable("c_{ends}", 20, "1/yard^2", "cost of box ends")
c_ferry = gpkit.Variable("c_{ferry}", 0.10, "-", "cost of ferry trip")

A_end = w*h
A_side = l*h
A_bottom = w*l

total_cost = c_ferry*V1/(l*w*h) + c_ends*2*A_end + c_sides*(2*A_side + A_bottom)

gp = gpkit.GP(total_cost)
sol = gp.solve()
print sol.table()

gp.sub(h, 1)
sol = gp.solve()
print sol.table()

A_scrap = gpkit.Variable("A_{scrap}", 4, "yards^2", "scrap material available")

gp = gpkit.GP(c_ferry*V1/(l*w*h) + c_ends*2*A_end,
              [2*A_side + A_bottom <= A_scrap])
gp

print gp.solve().table()

L = gpkit.Variable("L", 1, "yards", "total fence length")

l = gpkit.Variable("l", "yards", "plot side parallel to river")
w = gpkit.Variable("w", "yards", "plot side perpendicular to river")

A_plot = l*w

gp = gpkit.GP(1/A_plot, [2*w + l <= L])
sol = gp.solve()
print sol.table()

R = gpkit.Variable("R", 1, "inches", "log radius")

d = gpkit.Variable("d", "inches", "beam depth")
w = gpkit.Variable("w", "inches", "beam width")

gp = gpkit.GP(1/(w*d**3), [(d/2)**2 + (w/2)**2 <= R**2])
sol = gp.solve()
print sol.table()

L = gpkit.Variable("L", 1, "inches", "tin sheet side length")

l = gpkit.Variable("l", "inches", "box length")
w = gpkit.Variable("w", "inches", "box width")
h = gpkit.Variable("h", "inches", "box height")

cx = gpkit.Variable("c_x", "inches", "corner cutout length in x dimension")
cy = gpkit.Variable("c_y", "inches", "corner cutout length in y dimension")

gp = gpkit.GP(1/(l*w*h),
              [L >= w + 2*cx,
               L >= l + 2*cy,
               cx >= h,
               cy >= h])
sol = gp.solve()
print sol.table()

tw = gpkit.Variable("\\tau_W", "-", "hours spent working")
ts = gpkit.Variable("\\tau_S", "-", "hours spent sleeping")
to = gpkit.Variable("\\tau_O", "-", "hours spent eating and/or listening")
tm = gpkit.Variable("\\tau_M", "-", "hours spent listening to music")
s = gpkit.Variable("s", "-", "savings accrued per day")

p = gpkit.Variable("p", 0.5, "-", "pay rate per unit productivity")
c = gpkit.Variable("c", 5, "-", "cost of new records, per hour")
te = gpkit.Variable("\\tau_E", 3 ,"-", "hours required to be spent eating")

gp = gpkit.GP( 1/s,
              [p*tw**1.5*ts**0.75*tm**0.1 >= s + c*tm,
               tw + ts + to <= 24,
               to >= tm,
               to >= te])
sol = gp.solve()
print sol.table()

from IPython import utils
from IPython.core.display import HTML
import os
def css_styling():
    """Load default custom.css file from ipython profile"""
    base = utils.path.get_ipython_dir()
    styles = "<style>\n%s\n</style>" % (open(os.path.join(base,'profile_default/static/custom/custom.css'),'r').read())
    return HTML(styles)
css_styling()