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I have just learned the simplex method for solving linear programs, and I'm trying to understand what it's dual problem represents. I understand the mechanics of solving a dual problem - I do not need help with that. What I can't get (even after reading about it on Wikipedia ) is the actual meanings of the y variables in the dual . I would like to give an example all together with variable meanings in the primal problem, and what I figured out of the dual, and would ask anyone kind enough to explain the meanings in the dual: Primal: max z = 3*x1 + 5*x2 subject to: x1 <= 4 2*x2 <= 12 3*x1 + 2*x2 <= 18 x1, x2 >= 0 In the primal problem, x1 and x2 are quantities of products A and B to be produced. 3 and 5 are their unit selling prices, respectively. Products are produced on 3 machines, M1-M3 . To produce a first product, an hour of work on M1 and 3 hours on M3 are needed. To produce the second one, two hours of work are needed on both M2 and M3 . Machines M1, M2, M3 can work for maximum of 4, 12 and 18 hours, respectively. Finally, I can not produce a negative quantity of any of the products. Now, I set the dual problem: min z = 4*y1 + 12*y2 + 18*y3 subject to: y1 + 3*y3 >= 3 2*y2 + 2*y3 >= 5 y1, y2, y3 >= 0 Now, the only thing I think I can figure out is that the constraints mean: for an hour of work on M1 and 3 hours on M3 , I should get payed at least 3 money units for two hours of work on M2 and 2 hours on M3 , I should get pa

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