Hey I just found some difficulties in an old exam paper I tried to answer them with my classmate but we found some difficulties Could you help me please It is true and false 1- an active inequality constraint has zero slack or surplus , which means that optimal soloution satisfies the constraint with equality. (T&F) ? 2- A <= constraint with positive optimal slack will always have an infinite allowable increase for the RHS. (T&F) ? 3- Infeasibility as oppoesed to unboundedness, has nothing to do with OF. Thank you
asked
Bee1996 |

- The use of slack and surplus variables is as follows: value of constraint function - surplus + slack = right hand side. So if the slack and surplus are both 0, then ...
- I assume by "allowable increase" you mean how much the right side can increase
*while retaining the same value of the corresponding dual variable*. Think of the right side as some sort of resource. If the solver did not want to use the entire supply you had, what would change if you increased the supply? - Infeasibility means you cannot satisfy the constraints. If you cannot satisfy them with a given objective function, can you satisfy them if, say, the objective function is changed to zero (so all feasible solutions are equally good)?
answered
Paul Rubin ♦♦ |

I'm not going to do your homework, test or whatever. But I'll make a comment on 3 (I presume OF means objective function). The answer to this is not necessarily the same between a) exact arithmetic and b) the behavior of practical highly regarded commercial solvers using finite precision and pre-solve. Those who don't realize that can be in for a world of hurt.