Linear programming maximization code in MATLAB

Question

How to solve the linear programming maximization problem that contains both <= and >= equations?

For example here's a case:

Maximize:

z = c1x1 + c2x2 + c3x3

Subject to:

a1x1 + a2x2 + a3x3 <= b1
a4x1 + a5x2 + a6x3 <= b2
x1 >= d1
x2 >= d2
x3 >= d3

Where a1, a2, a3, a4, a5, a6, b1, b2, b3, c1, c2, c3 are the constants in the given equations.

What will be the proper Matlab code to solve this problem?

Sardar Usama · Accepted Answer · 2016-05-26 18:03:13Z

1

That's how :

    z = -[c1 ; c2 ; c3];

    A = [ a1 a2 a3 ; 
          a4 a5 a6]; 

    b=[b1;
       b2];

    Aeq= [ ]; beq= [ ];

    LB = [d1 ; d2 ; d3]; 

    UB = [1 ; 1 ; 1]* inf; % Any relax number

    x = linprog(z, A, b, Aeq, beq, LB, UB)

answered May 26, 2016 at 18:03

Sardar Usama

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7 Comments

Tiash Over a year ago

Thanks @Sardar_Usama, How can I get the value of z using matlab?

Sardar Usama Over a year ago

By putting the values of constants c1 , c2 and c3

Tiash Over a year ago

Do I have to calculate it manually or is there any built-in function to do that?

Sardar Usama Over a year ago

What exactly are you asking?

Sardar Usama Over a year ago

if you're asking for the value of this: z = c1x1 + c2x2 + c3x3 , it doesn't mean anything since x1,x2 andx3 are decision variables. You can find the value of z by putting the different values of these variables and constants c1,c2 and c3. And if you want to find the maximum value of z, it is already given in the code.

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