1 | initial version |

I have a partial answer for you. I can get the matrix constraints to work as in the following example:

```
p = MixedIntegerLinearProgram(maximization = True, solver='GLPK')
x = p.new_variable(real=True,nonnegative=True)
M=Matrix([[1,0.2],[1.5,3]])
v = vector([4,4])
u = vector([1,5])
p.add_constraint(M*x <= v)
p.show()
```

Unfortunately, I cannot get the objective function to work so nicely with vectors. I cannot seem to get set_objective to let me do a vector calculation inside the command.

Another option is to work with `linear_program`

as found at http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html

2 | No.2 Revision |

I have a partial answer for you. I can get the matrix constraints to work as in the following example:

```
p = MixedIntegerLinearProgram(maximization = True, solver='GLPK')
x = p.new_variable(real=True,nonnegative=True)
M=Matrix([[1,0.2],[1.5,3]])
v = vector([4,4])
u = vector([1,5])
p.add_constraint(M*x <= v)
p.show()
```

Unfortunately, I cannot get the objective function to work so nicely with vectors. I cannot seem to get set_objective to let me do a vector calculation inside the command.

Another option is to work with `linear_program`

as found at http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html

I think @Nathann is one of the experts on the linear programming in Sage.

3 | No.3 Revision |

I have a partial answer for you. I can get the matrix constraints to work as in the following example:

```
p = MixedIntegerLinearProgram(maximization = True, solver='GLPK')
x = p.new_variable(real=True,nonnegative=True)
M=Matrix([[1,0.2],[1.5,3]])
v = vector([4,4])
u = vector([1,5])
p.add_constraint(M*x <= v)
p.show()
```

Unfortunately, I cannot get the objective function to work so nicely with vectors. I cannot seem to get set_objective to let me do a vector calculation inside the command.

Another option is to work with `linear_program`

as found at http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html

I think @Nathann is one of the experts on the linear programming in ~~Sage.~~Sage. He definitely would know more.

For the `linear_program`

command, here is some sample code:

```
M=Matrix(RDF,[[-1,0],[0,-1],[-1,-1] ])
v = vector(RDF,[-5.5,-3.5,-7.5])
u = vector(RDF,[3,4])
sol=linear_program(u,M,v)
sol['x']
```

This solves: $M x \ge v$ with the objective function $u^t x$.

4 | No.4 Revision |

```
p = MixedIntegerLinearProgram(maximization = True, solver='GLPK')
x = p.new_variable(real=True,nonnegative=True)
M=Matrix([[1,0.2],[1.5,3]])
v = vector([4,4])
u = vector([1,5])
p.add_constraint(M*x <= v)
p.show()
```

`linear_program`

as found at http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html

I think @Nathann is one of the experts on the linear programming in Sage. He definitely would know more.

For the `linear_program`

command, here is some sample code:

```
M=Matrix(RDF,[[-1,0],[0,-1],[-1,-1] ])
v = vector(RDF,[-5.5,-3.5,-7.5])
u = vector(RDF,[3,4])
sol=linear_program(u,M,v)
sol['x']
```

This ~~solves: ~~minimizes: $M x \ge v$ with the objective function $u^t x$.

5 | No.5 Revision |

```
p = MixedIntegerLinearProgram(maximization = True, solver='GLPK')
x = p.new_variable(real=True,nonnegative=True)
M=Matrix([[1,0.2],[1.5,3]])
v = vector([4,4])
u = vector([1,5])
p.add_constraint(M*x <= v)
p.show()
```

`linear_program`

as found at http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html

I think @Nathann is one of the experts on the linear programming in Sage. He definitely would know more.

For the `linear_program`

command, here is some sample code:

```
M=Matrix(RDF,[[-1,0],[0,-1],[-1,-1] ])
v = vector(RDF,[-5.5,-3.5,-7.5])
u = vector(RDF,[3,4])
sol=linear_program(u,M,v)
sol['x']
```

This ~~minimizes: $M x \ge v$ with ~~minimizes the objective function $u^t ~~x$.~~x$ with constraint $M x \ge v$.

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