Posted by Gopala Tumuluri on September 27, 1998 at 23:26:30:
In Reply to: Negative sign in shadow price posted by Min Zhang on September 27, 1998 at 19:29:54:
: What does the negative sign in shadow price mean?
: Does it means that if we increase slack variable by x units the cost/profit (whatever we were maximizing) will decrease (?) by Shadow Price * x?
Shadow price tells you the direction and the magnitude of the change the objective will experience when the corresponding slack variable is INCREASED (remember the shadow price considers positive deltas).
For a cost minimization problem, a negative shadow price means that an increase in the corresponding slack variable results in a decreased cost. If the slack variable decreases then it results in an increased cost (because negative times negative results in a positive).
The magnitude of the change is given by the value of the shadow price. The sign gives the direction of the change.
Can anyone correct me or add something to what I said?
Thanks
Gopala