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simplex

 feasible
 determine if system is feasible or not

 Calling Sequence feasible(C) feasible(C, vartype) feasible(C, vartype, 'NewC', 'Transform')

Parameters

 C - set of linear constraints vartype - (optional) NONNEGATIVE or UNRESTRICTED NewC - (optional) name Transform - (optional) name

Description

 • The function feasible returns true if a feasible solution to the linear system C exists, and false otherwise.
 • Non-negativity constraints on all the variables can be indicated by use of a second argument, NONNEGATIVE, or by explicitly listing the constraints. No restriction on the signs of the variable may be indicated by using UNRESTRICTED as the second argument to feasible.
 • The final two arguments are used to return, as sets, the final system found by feasible, and any variable transformations which occurred. The new system may have global artificial and slack variables present (such as  _AR or _SL1).
 • The command with(simplex,feasible) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{simplex}\right):$
 > $\mathrm{feasible}\left(\left\{4x+3y\le 5,3x+4y=4\right\},\mathrm{NONNEGATIVE}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{feasible}\left(\left\{4x-3y\le 5,3x-4y=4,0\le x,0\le y\right\}\right)$
 ${\mathrm{false}}$ (2)