Linnear programming system of equations and restrictions While doing a linnear programming problem, i came with this system of equations of 10 variables, and 7 restrictions (7 equations and 10 inequalities).
The objtective is to minimize the function:
$$Z=3x_{14}+5x_{15}+8x_{25}+9x_{23}+2x_{45}+4x_{35}+2x_{46}+5x_{56}+7x_{57}+2x_{37}$$
Subject to:
$437.5=x_{14}+x_{15}$
$437.5=x_{25}+x_{23}$
$x_{23}=x_{35}+x_{37}$
$x_{14}=x_{45}+x_{46}$
$x_{15}+x_{25}=x_{56}+x_{57}$
$x_{46}+x_{56}=600$
$x_{57}+x_{37}=275$
And
$x14≤300$
$x15≤300$
$x25≤300$
$x23≤200$
$x45≤200$
$x35≤200$
$x46≤300$
$x56≤300$
$x57≤300$
$x37≤200$
There are programms wich are suposed to solve this, but no one recives equations as an innput.
What can i do?
 A: There are many linear programming solvers available.  Look at Wikipedia, for example.  I would think that nearly all of these would accept equations as well as inequalities.  But if by some chance you're stuck with a program that only accepts inequalities, you can replace each equation $a = b$
by the pair of inequalities $a \le b$ and $a \ge b$
A: I have good experiences with LINGO from LINDO Systems. A free version (6 months) can be downloaded here. 
$\color{blue}{\texttt{Input example}}$
$MAX \ \ 5 X1 + 7 X2 \\
    ST \\
    3 X1 + 4 X2 < 650\\
    2 X1 + 3 X2 < 500$
The default setting for the variables is, that they are non-negative. 
$X1, \ X2 \geq 0$
$\color{blue}{\texttt{Output example}}$
 Global optimal solution found.
  Objective value:                              1137.500
  Infeasibilities:                              0.000000
  Total solver iterations:                             1
  Elapsed runtime seconds:                         17.99

  Model Class:                                        LP

  Total variables:                      2
  Nonlinear variables:                  0
  Integer variables:                    0

  Total constraints:                    3
  Nonlinear constraints:                0

  Total nonzeros:                       6
  Nonlinear nonzeros:                   0



                                Variable           Value        Reduced Cost
                                      X1        0.000000           0.2500000
                                      X2        162.5000            0.000000

                                     Row    Slack or Surplus      Dual Price
                                       1        1137.500            1.000000
                                       2        0.000000            1.750000

                                   3        12.50000            0.000000

