#import std
#import nat
#import flo
#import lin

#import nat

items = # name: (weight,value)

<
   'map': (9,150),
   'compass': (13,35),
   'water': (153,200),
   'sandwich': (50,160),
   'glucose': (15,60),
   'tin': (68,45),
   'banana': (27,60),
   'apple': (39,40),
   'cheese': (23,30),
   'beer': (52,10),
   'suntan cream': (11,70),
   'camera': (32,30),
   't-shirt': (24,15),
   'trousers': (48,10),
   'umbrella': (73,40),
   'waterproof trousers': (42,70),
   'waterproof overclothes': (43,75),
   'note-case': (22,80),
   'sunglasses': (7,20),
   'towel': (18,12),
   'socks': (4,50),
   'book': (30,10)>

system =

linear_system$[
   binaries: ~&nS,
   lower_bounds: {'(slack)': 0.}!,
   costs: * ^|/~& negative+ float@r,
   equations: ~&iNC\400.+ :/(1.,'(slack)')+ * ^|rlX/~& float@l]

#show+

main = ~&tnS solution system items