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# 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: Parametes:

 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)