Use CPLEX to Solve a Linear Programming (LP) Problem

The Problem:

Max: z = 3x1 + 2x2
Subject to:
        2x1 + x2 <= 100
        x1 + x2 <= 80
        x1 <= 40
        0 <= x1
        0 <= x2

Method #1:

CPLEX> enter example
Enter new problem ['end' on a separate line terminates]:
maximize 3 x1 + 2 x2
subject to 2 x1 + x2 <= 100
x1 + x2 <= 80
x1 <= 40
x1 >= 0
x2 >= 0
end

CPLEX> optimize
Tried aggregator 1 time.
LP Presolve eliminated 3 rows and 0 columns.
Reduced LP has 2 rows, 2 columns, and 4 nonzeros.
Presolve time = 0.00 sec.

Iteration log . . .
Iteration: 1 Dual infeasibility = 0.500000
Iteration: 3 Dual objective = 180.000000

Dual simplex - Optimal: Objective = 1.8000000000e+02
Solution time = 0.00 sec. Iterations = 3 (2)

CPLEX> display solution variables x1-x2
Variable Name Solution Value
x1 20.000000
x2 60.000000

CPLEX>

Method #2 (using bounds statements):

CPLEX> enter example
Enter new problem ['end' on a separate line terminates]:
maximize 3 x1 + 2 x2
subject to 2 x1 + x2 <= 100
x1 + x2 <= 80
x1 <= 40
bounds
0 <= x1
0 <= x2
end

CPLEX> optimize
Tried aggregator 1 time.
LP Presolve eliminated 1 rows and 0 columns.
Reduced LP has 2 rows, 2 columns, and 4 nonzeros.
Presolve time = 0.00 sec.

Iteration log . . .
Iteration: 1 Dual infeasibility = 0.500000
Iteration: 3 Dual objective = 180.000000

Dual simplex - Optimal: Objective = 1.8000000000e+02
Solution time = 0.00 sec. Iterations = 3 (2)

CPLEX> display solution variables x1-x2
Variable Name Solution Value
x1 20.000000
x2 60.000000

CPLEX>

last update: July 03, 2009