Example

In this example we solve the following sample problem from MATLAB’s documentation page on the linprog function.

Find x that minimizes

f(x) = –5x₁ – 4x₂ –6x₃,

subject to

x₁ – x₂ + x₃ ≤ 20
3x₁ + 2x₂ + 4x₃ ≤ 42
3x₁ + 2x₂ ≤ 30
0 ≤ x₁, 0 ≤ x₂, 0 ≤ x₃.

First, enter the coefficients:

>> f = [-5; -4; -6];
>> A = [1 -1  1
>>      3  2  4
>>      3  2  0];
>> b = [20; 42; 30];
>> lb = zeros(3,1);

Next, call the Xpress Optimizer linear programming optimization function xprslp.

>> [x,fval,exitflag,output,lambda] = xprslp(f,A,b,'L',lb);

Entering x, lambda.lin, and lambda.lower returns the following results:

x = 
     0.0000
    15.0000
     3.0000
lambda.lin =
     0
     1.5000
     0.5000
lambda.lower =
     1.0000
     0
     0