linopt::plot_data

Plot the feasible region of a linear program

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

linopt::plot_data([constr, obj, <NonNegative>, <seti>], vars)
linopt::plot_data([constr, obj, <NonNegative>, <All>], vars)
linopt::plot_data([constr, obj, <setn>, <seti>], vars)
linopt::plot_data([constr, obj, <setn>, <All>], vars)

Description

linopt::plot_data([constr, obj], vars) returns a graphical description of the feasible region of the linear program [constr, obj], and the line vertical to the objective function vector through the corner with the maximal objective function value found.

[constr, obj] is a linear program with exactly two variables. The problem has the same structure like in linopt::maximize. The second parameter vars specifies which variable belongs to the horizontal and vertical axis.

Examples

Example 1

We plot the feasible region of the given linear program. Here the valid corners of the linear program are easy to see:

k := [{2*x + 2*y >= 4, -2*x + 4*y >= -2, -2*x + y >= -8,
       -2*x + y <= -2, y <= 6}, x + y, NonNegative]:
g := linopt::plot_data(k, [x, y]):
plot(g):

In this example there is no difference if the Option NonNegative is given for the linear program or not:

k := [{2*x + 2*y >= 4, -2*x + 4*y >= -2, -2*x + y >= -8,
       -2*x + y <= -2, y <= 6}, x + y]:
g := linopt::plot_data(k, [x, y]):
plot(g):

delete k, g:

Example 2

Now we give an example where one can see a difference if the variables are constrained to be nonnegative:

k := [{x + y >= -1, x + y <= 3}, x + 2*y]:   
g := linopt::plot_data(k, [x, y]):
plot(g):

k := [{x + y >= -1, x + y <= 3}, x + 2*y, NonNegative]:
g := linopt::plot_data(k, [x, y]):
plot(g):

delete k, g:

Parameters

constr

A set or list of linear constraints

obj

A linear expression

seti

A set which contains identifiers interpreted as indeterminates

setn

A set which contains identifiers interpreted as indeterminates

vars

A list containing the two variables of the linear program described by constr and obj and the existing options

Options

All

All variables are constrained to be integer

NonNegative

All variables are constrained to be nonnegative

Return Values

Expression describing a graphical object which can be used by plot.

References

Papadimitriou, Christos H; Steiglitz, Kenneth: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, 1982.

Nemhauser, George L; Wolsey, Laurence A: Integer and Combinatorial Optimization. New York, Wiley, 1988.

Salkin, Harvey M; Mathur, Kamlesh: Foundations of Integer Programming. North-Holland, 1989.

Neumann, Klaus; Morlock, Martin: Operations-Research. Munich, Hanser, 1993.

Duerr, Walter; Kleibohm, Klaus: Operations Research; Lineare Modelle und ihre Anwendungen. Munich, Hanser, 1992.

Suhl, Uwe H: MOPS - Mathematical OPtimization System. European Journal of Operational Research 72(1994)312-322. North-Holland, 1994.

Suhl, Uwe H; Szymanski, Ralf: Supernode Processing of Mixed Integer Models. Boston, Kluwer Academic Publishers, 1994.

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