# Attempting to solve a linear program using Maxima, but problem unbounded.

As the title says, I'm attempting to use Maxima's minimize_lp(objective,conditions,nonegative=true) to solve a linear program, where the function $$z(x_1,x_2,x_3) = 10x_1 + 4x_2 + 5x_3$$ is to be minimized with the conditions \begin{align} 5x_1 - 7x_2 + 3x_3 &\geq 50,\\ x_1,x_2,x_3 &\geq 0\,. \end{align} However, I'm getting the Problem not bounded! error as a result, and wondering what the cause of this is. Surely the problem is not unbounded? If it is, is it possible to see it right from the start? I'm really rusty on matrix algebra and have't actually taken a course in optimization methods, so I have no idea what to look for here.

• Is this $$x_1$$ in your second line? – Dr. Sonnhard Graubner Oct 19 '18 at 14:19
• Yes, let me fix that. – SeSodesa Oct 19 '18 at 14:20
• The problem is not unbounded. See here Have you tried to solve the problem with the simplex method? – callculus Oct 19 '18 at 14:38
• it is immediate that the objective value cannot drop below 0 – LinAlg Oct 19 '18 at 15:04
• I think the reason is a typo in the statement. minimize_lp(10*x1+4*x2+5*x3,[5*x1−7*x2+3*x3>=50,x1>=0,x2>=0,x3≥0]); will work but minimize_lp(10*x1+4*x2+5*x3,[5*x1−7*x2+3*x3>=50,x>=0,x2>=0,x3≥0]); will raise this error because x1 is not bounded now. – miracle173 Jan 13 at 14:50

• Looks like I've once again failed to read the documentation properly. It was the nonegative=true inside the function that caused the issue. – SeSodesa Oct 19 '18 at 15:51