Question

Please answer “true”, “false”, or “it depends” with an explanation as to why.

1. It is ok to run a linear programming problem without constraints. After all, this is capitalism and there are no constraints.

2. The optimal answer to a linear programming problem always has no slack.

3. Given a linear programming optimization problem, with the choice of two products, we know in advance that a possible answer is to make only one product.  

Cost minimization problems typically involve constraints that have the phrase “at least”.

Answer 1

1.

False

Without a constraint, a linear program becomes unbounded i.e. it can be maximized or minimized up to infinity. it is pretty much useless to deal with such situations.

2.

False

At optimality, some constraints may have slack. These are called the non-binding constraints. The other constraints will have zero slack, these the binding constraints.

3.

False

'Possible' means feasible. An LP may have infeasibility. So, even when we have two products to produce, it is very well possible that none of them can be feasibility produced depending on the set of constraints.

4.

It depends.

The minimization problems 'generally' associated with '>=' or 'at-least' constraints. But there can be other constraints of '<=' or '=' type as well.