Hello,
This thread is about the solving Linear/Non linear Programming problem. 
This topic is related to Optimization Technique, Operations Research.
Linear programming (LP) (also called linear optimization) is a method to 
achieve the best
outcome (such as maximum profit or lowest cost) in a mathematical model 
whose requirements are represented by
linear relationships. Linear programming is a special case of mathematical 
programming (mathematical optimization).
Currently I don't see any method to solve these kinds of problems in SymPy. 
Most of the time we use simplex method or its
expansion to solve them.

Example:

Maximize z = 12x+40y
subjected to :
  x+y<=16
  x+3y<=36
  x<=10
  x>=0
  y>=0

find x,y and maximum value of z.
Soln : (x, y) = (0,12) and maxi value at this point is 480.

Let me know if there is already some way to solve these using SymPy methods 
or it is good idea to implement it.

Related links :
Linear Programming: https://en.wikipedia.org/wiki/Linear_programming
Simplex method: https://en.wikipedia.org/wiki/Simplex_algorithm
Wolfram: 
http://reference.wolfram.com/language/tutorial/ConstrainedOptimizationLinearProgramming.html
SciPy: 
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html
Other tools: 
http://stackoverflow.com/questions/10697995/linear-programming-in-python

--
Shekhar

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