Sam has been assigned the task of completing a production and shipping plan model. Sam knows to follow these rules for the shipping plan part of the model.

Balance: Supply = Demand

Supply and demand constraints are (=)

Unbalance: Supply > Demand

Supply constraints are ()

Demand constraints are (=)

Unbalance: Supply < Demand

Supply constraints are (=)

Demand constraints are ()

She have multiple scenarios that she have to investigate for the production plan. Each scenario significantly changes the supply amounts. She is required to change the supply and demand signs for each scenario which is time consuming. Sam reasons that () means ">" and "=" are both possible. Likewise, ()means "<" and "=" are both possible. Therefore, it seems logical to Sam that using () supply and ()demand for all scenarios will save her time because this sign combination will account all balance and unbalance options which may occur for each scenario.

Explain why Sam's use of these signs combination logic is flawed in physical terms of product units flowing out from the origins and flowing into the destinations with the objective of creating the lowest cost shipping plan.