Package com.imsl.test.example.math

Class DenseLPEx3

java.lang.Object

com.imsl.test.example.math.DenseLPEx3

public class DenseLPEx3
extends Object

Solves a linear programming problem in \(5\) variables.

This example solves the following linear programming problem:

$${\rm {max}} \,\, f(x) = 10x_1 + 15x_2 + 15x_3 + 13x_4 + 9x_5$$

subject to the following set of constraints,

$$ \begin{array}{cc} 100x_1 + 50x_2 + 50x_3 + 40x_4 + 120x_5 &\le& 300\\ 40x_1 + 50x_2 + 50x_3 + 15x_4 + 30x_5 &\le& 40 \end{array} $$

and bounds: $$0.0 \le x_i \le 1.0, i=1,2,\ldots,5$$

Note that since DenseLP minimizes, the sign of the objective function must be changed to compute this solution. The signs of the dual solution components and the optimal value must also be changed. Because \(x_2\) and \(x_3\) are not uniquely determined within the bounds, this problem has a convex family of solutions. DenseLP issues an exception, MultipleSolutionsException. A particular solution is available and retrieved in the finally block.

See Also:

• Code
• Output

Constructor Summary

Constructors

Constructor	Description
DenseLPEx3()

Method Summary

Modifier and Type	Method	Description
static void	main(String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

DenseLPEx3

public DenseLPEx3()

Method Details

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception