Let’s first define the standard format of linear programming problem,

in which we will minimize the following equation

$$

z=CX

$$

where， C is the vector of coefficients，X is the vector of variables to be optimized.

The constraints of this minimization can be written as:

$$

AX<=B

$$

where，A and B are both coefficient matrix。

Let’s see an specific example：

$$

min , z=10x_1 +15x_2+25x_3

\s.t

\-1x_1-1x_2-1x_3<=-1000

\-1x_1+2x_2-0x_3<=0

\0x_1+0x_2-1x_3<=-300

\-1x_1<=0

\-1x_2<=0

\-1x_3<=0

$$

In Python, we could call the linprog function in Scipy package to solove linear programming problem,

and here is a simple demo of coding in Python:

# Import required libraries |

```
Optimal value: 14500.0
x values: [7.0000000e+02 7.1017063e-09 3.0000000e+02]
Number of iterations performed: 7
Status: Optimization terminated successfully.
```