maximize - Maple Help

simplex

 maximize
 maximize a linear program

 Calling Sequence maximize(f, C) maximize(f, C, vartype) maximize(f, C, vartype, 'NewC', 'transform')

Parameters

 f - linear expression C - set or list of linear constraints vartype - (optional) NONNEGATIVE or UNRESTRICTED NewC - (optional) name transform - (optional) name

Description

 • The expression f is the linear objective function to be maximized subject to the linear constraints C. The function maximize returns either a set of equations describing the optimal solution to the specified linear program, or the empty set in the case where no feasible solution to C exists, or NULL in the case where the solution is unbounded.
 • The equations returned by maximize can be substituted back into the objective function f to obtain the value of the objective function at the optimal solution.
 • A third parameter may be used to specify that all variables are constrained to be NONNEGATIVE; such constraints may also be listed explicitly. Similarly, UNRESTRICTED indicates that no sign constraint is to be placed on the variables.
 • A fourth and a fifth parameter may be included to specify names for returning the optimal description, and any variable transformations used to set up the problem.
 • The Optimization[LPSolve] command also computes solutions to linear programs.  It is generally more efficient than the simplex[minimize] command, but performs all its computations using floating-point values.
 • The command with(simplex,maximize) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{simplex}\right):$
 > $\mathrm{maximize}\left(x+y,\left\{3x+4y\le 4,4x+3y\le 5\right\}\right)$
 $\left\{{x}{=}\frac{{8}}{{7}}{,}{y}{=}\frac{{1}}{{7}}\right\}$ (1)
 > $\mathrm{maximize}\left(x-y,\left\{3x+4y\le 4,4x+3y\le -3\right\}\right)$
 > $\mathrm{maximize}\left(x-y,\left\{3x+4y\le 4,4x+3y\le -3\right\},\mathrm{NONNEGATIVE}\right)$
 ${\varnothing }$ (2)