=== 1. Box Transport ===

       ┃┓
       ┃┃
       ┃┃
       ┃┣╸1/h/length/w
       ┃┃ (1)
       ┃┃
       ┃┛
  Cost╺┫┓
 (100) ┃┣╸h·w
       ┃┛ (0.5)
       ┃┓
       ┃┣╸h·length
       ┃┛ (1)
       ┃┓
       ┃┣╸length·w
       ┃┛ (2)



              ┃┓
              ┃┃
              ┃┣╸V1 = 400
              ┃┃
              ┃┛
              ┃┓
              ┃┃
 BoxTransport╺┫┣╸c_ferry = 0.1
              ┃┃
              ┃┛
              ┃┓
              ┃┃
              ┃┣╸c_sides = 10
              ┃┛
              ┃┣╸c_ends = 20
              ┃┛


Optimal Cost
------------
BoxTransport.c_ferry·BoxTransport.V1/(BoxTransport.length·BoxTransport.w·BoxTransport.h) + BoxTransport.c_ends·2·BoxTransport.w·BoxTransport.h + BoxTransport.c_sides·(2·BoxTransport.length·BoxTransport.h + BoxTransport.w·BoxTransport.length) : 100

Solution
--------
BoxTransport
      h : 0.5         box height
 length : 2           box length
      w : 1           box width
...constants
c_sides : 10   (+0.4) cost of box sides and bottom (per unit area)
     V1 : 400  (+0.4) volume of gravel to transport
c_ferry : 0.1  (+0.4) cost per ferry trip
 c_ends : 20   (+0.2) cost of box ends (per unit area)

=== 2. Fence Plot ===

      ┃┓
 Cost╺┫┃
  (8) ┃┣╸1/(length·w)
      ┃┛ (8)



           ┃┓
           ┃┃
           ┃┣╸L = 1
 FencePlot╺┫┛
           ┃┓
           ┃┃
           ┃┣╸L ≥ 2·w + length
           ┃┛


Optimal Cost
------------
1/(FencePlot.length·FencePlot.w) : 8

Solution
--------
FencePlot
length : 0.5        plot side parallel to river
     w : 0.25       plot side perpendicular to river
...constants
     L : 1     (-2) total fence length

=== 3. Beam Cross-Section ===

         ┃┓
    Cost╺┫┃
 (0.192) ┃┣╸1/(w·d³)
         ┃┛ (0.192)



                  ┃┓
                  ┃┃
                  ┃┣╸R = 1
 BeamCrossSection╺┫┃
                  ┃┛
                  ┃┓
                  ┃┣╸R² ≥ (d/2)² + (w/2)²
                  ┃┛


Optimal Cost
------------
1/(BeamCrossSection.w·BeamCrossSection.d³) : 0.1925

Solution
--------
BeamCrossSection
d : 1.732       beam depth
w : 1           beam width
...constants
R : 1      (-4) log radius

=== 4. Box from Sheet ===

        ┃┓
   Cost╺┫┃
 (13.5) ┃┣╸1/(length·w·h)
        ┃┛ (13.5)



              ┃┓
              ┃┃
              ┃┃
              ┃┃
              ┃┃
              ┃┣╸L = 1
              ┃┃
              ┃┃
              ┃┃
 BoxFromSheet╺┫┛
              ┃┓
              ┃┃
              ┃┣╸L ≥ length + 2·cy
              ┃┛
              ┃┓
              ┃┃
              ┃┣╸L ≥ w + 2·cx
              ┃┛
              ┃┣╸cx ≥ h
              ┃┣╸cy ≥ h


Optimal Cost
------------
1/(BoxFromSheet.length·BoxFromSheet.w·BoxFromSheet.h) : 13.5

Solution
--------
BoxFromSheet
    cx : 0.1667       corner cutout length in x dimension
    cy : 0.1667       corner cutout length in y dimension
     h : 0.1667       box height
length : 0.6667       box length
     w : 0.6667       box width
...constants
     L : 1       (-3) tin sheet side length

=== 5. Work/Sleep Allocation ===

           ┃┓
      Cost╺┫┃
 (0.00901) ┃┣╸1/s
           ┃┛ (0.00901)



           ┃┓
           ┃┃
           ┃┃
           ┃┃
           ┃┃
           ┃┣╸tw + ts + to ≤ 24
           ┃┃
           ┃┃
           ┃┃
 WorkSleep╺┫┛
           ┃┓
           ┃┃
           ┃┣╸p = 0.5
           ┃┛
           ┃┓
           ┃┃
           ┃┣╸p·tw^1.5·ts^0.75·tm^0.1 ≥ s + c·tm
           ┃┛
           ┃┣╸te = 3
           ┃┣╸to ≥ te


Optimal Cost
------------
1/WorkSleep.s : 0.009006

Solution
--------
WorkSleep
 s : 111              savings accrued per day
tm : 2.467            hours spent listening to music
to : 3                hours spent eating and/or listening
ts : 7                hours spent sleeping
tw : 14               hours spent working
...constants
 p : 0.5    (-1.111)  pay rate per unit productivity
te : 3      (+0.3571) hours required for eating
 c : 5      (+0.1111) cost of new records per hour
