Why I get the minus result for linear optimization?

I am trying to solve a linear optimization problem, and I have followed the steps of the guide in MATLAB website. And I get the minus result. I am pretty sure the max is 36000.

    linearOptim = optimproblem('ObjectiveSense','maximize');
    product_1 = optimvar('product_1', 'Type', 'integer', 'LowerBound', 0);
    product_2 = optimvar('product_2', 'Type', 'integer', 'LowerBound', 0);
    linearOptim.Objective = 3000 * product_1 + 5000 * product_2;
    linearOptim.Constraints.econs1 = product_1 <= 4;
    linearOptim.Constraints.econs2 = 2 * product_2 <= 12;
    linearOptim.Constraints.econs3 = 3 * product_1 + 2 * product_2 <= 18;
    showproblem(linearOptim);
    solveLinearOptim = solve(linearOptim);

[Walter Roberson]

It is common to handle maximizations by minimizing the negative of the function. When maximizations are done this way, you have to take the negative of the output value.

Your code produces a value of -36000 which is exactly the negative of what you are expecting.

[Edward Xu]

Got it. Thank you. But I think it’s better if the software can express the output value based on the exact input objective function, or just tell the user the reason, isn’t it?

[Torsten]

But how to tell the software that you wanted to maximize instead of minimize ?

[Walter Roberson]

Torsten, the new problem based optimization permits that. Notice Edward included

      linearOptim = optimproblem('ObjectiveSense','maximize');

I think it would be quite reasonable for the optimizer to get the sign right in such a case, but it does not appear to do so.

Answer 1

[Alan Weiss]

You are seeing the underlying solver's intermediate calculations. But if you look at the returned function value, you get the correct answer. For example,

evaluate(linearOptim.Objective,solveLinearOptim)
ans =

       36000

Or even more simply, in the function call itself:

[solveLinearOptim,fval] = solve(linearOptim)

    LP:  Optimal objective value is -36000.000000. % This is the confusing bit
  **snip**
  solveLinearOptim = 

    struct with fields:

      product_1: 2.0000
      product_2: 6

fval =

         36000 % This is the correct answer

Alan Weiss

MATLAB mathematical toolbox documentation