python - Linear Programming with cvxpy

Question

I would like to ask you regarding on the Linear Program for optimization.

I have an objective function, and constraint functions as below,

• variables(x1, x2, x3, x4, x5, x6) are quantities of the products, and the quantities of products have to be fixed numbers now.

• the goal of this problem is the optimizing the quantities of products.

  1. Objective Function (c.T * [x1, x2, x3, x4, x5, x6])

     [[c11, c12, c13, c14, c15 c16],
     
     [c21, c22, c23, c24, c25, c26],
                                   X     [x1, x2, x3, x4, x5, x6]  
     [c31, c32, c33, c34, c35, c36],
     
     [c41, c42, c43, c44, c45, c45]]
     

  The result that I would like to optimize is going to be as below

  c11*x1 + c12*x2 + c13*x3 + c14*x4 + c15*x5 + c16*x6 +
  c21*x1 + c22*x2 + c23*x3 + c24*x4 + c25*x5 + c26*x6 + 
  c31*x1 + c32*x2 + c33*x3 + c34*x4 + c35*x5 + c36*x6 + 
  c41*x1 + c42*x2 + c43*x3 + c44*x4 + c45*x5 + c46*x6 = optimized value
  

  2. Constraint Function

  1) constraint_1

  5500000*x1+2500000*x2+825000*x3+5500000*x4+5500000*x5+5500000*x6 <= 800000000

  2) constraint_2

  x1 <= 10
  x2 <= 10
  x3 <= 10
  x4 <= 10
  x5 <= 10
  x6 <= 10
  

The problem that I am suffering from is the in the "Objective Function of Cs(c1,1 ~ c4,5)".

I have solved the Linear Programming that has integers values in the Objective Functions, but not the matrix.

I have tried all other ways that I could, but now I really need helps on this.

Please kindly suggest me any kind of ideas or codes for this question.

Answer 1

Suppose you have store the original cij in a numpy array, you might like to sum up terms like c11+c21+c31+c41 first. This can be done by summing up each column, try c.sum(axis = 0)

>>> import numpy as np
>>> c = np.arange(24).reshape(4,6)
>>> c
array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23]])
>>> c = c.sum(axis=0)
>>> c
array([36, 40, 44, 48, 52, 56])