lineplan()

Description:

The external library function is for linear programming and calculates the minimum value in linear objective function under linear constraints.

Syntax:

lineplan(A,B,C)

Note:

The function uses simplex method to solve regular linear programming problems as well as problems where the basic solution isn’t a feasible solution (see example: the special problem). The problem needs to be converted to the following standard form when getting parameters:

 

Target function:

Linear inequality constraints:

Parameters:

A

A sequence representing coefficient matrix

B

A sequence representing a constraints matrix

C

The objective function matrix

Return value:

A sequence. Note the method of getting the target result. When trying to output the minimum value and its coordinates, the former is to multiply the first number of the first sub-sequence by -1, and the coordinates are the first n numbers of the second sub-sequence, where n is the number of x.

Example:

Here are how to solve simple linear programming problems defined by linear inequalities:

Regular problems:

 

A

 

1

[[2,1],[1,1],[0,1]]

Input coefficient matrix A

2

[[10,0],[8,0],[7,0]]

Input constraints matrix B

3

[[-4,-3],[0,0],[0,0]]

Input objective function matrix C

4

=lineplan(A1,A2,A3)


Get the result: the objective function’s minimum value is -26 and its coordinates are (2.0,6.0)

 

The special problem:

 

A

 

1

[[1,1],[-1,-1]]

Input coefficient matrix A

2

[[2,0],[-1,0]]

Input constraints matrix B

3

[[1,2],[0,0]]

Input objective function matrix C

4

=lineplan(A1,A2,A3)

Get the result: the objective function’s minimum value is 1 and its coordinates are (1.0,0.0)