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Hi John
I was going through a revision kit. For linear programming, sometimes there is a shadow price, sometimes a slack. The question always ask for a shadow price, though the answer may be a slack for one variable (or both?). My question is, how do we know when to check for slack (by inputting the optimal amounts into the constrain equation)?
I hope this makes sense.
I don’t know which Revision Kit you are using (and whether it is a current edition), but questions do not always ask for the shadow price. However, if there is a linear programming question in Section C of the exam, then certainly it is very likely to include asking for the shadow price.
Slack is rarely asked for in the exam, but slack is where at the optimal solution, one (or more) of the limited resources is not being used in full – it is the difference between the amount actually used and the amount available. If there is slack in one of the resources, then that resource does not have a shadow price because buying more of the resource would not change the result. There is no need to check for slack (unless it is specifically required) – obviously only those constraints that are binding at the optimal solution will have a shadow price.
Have you watched my free lectures on linear programming (because I do explain both shadow prices and slack)?
Hi John,
I did indeed watch some of your lectures on linear programming and I understand everything you have described above.
I am using a BPP revision kit.
What I mean is, the question will say “find the shadow price of these two constraints” but the answers sometimes show there is no shadow price, only slack (which is the answer to be given).
Where this happens, the answers show to substitute the optimal amounts into the constraint equation, where it comes up with a total that is less than the constraint maximum (this means there is slack). Again I understand this.
But in answers where there is no slack, no substitution like the above takes place. they just show the normal shadow price method with the equations.
what i mean is, how do we know when to check for slack?
As I wrote before, you only need to check for slack if the question asks you to. Assuming you are using a current edition of the BPP Kit then say one of the questions that is bothering you, then I will find the question and explain.
Hi John. Thank you for your response.
I am using a kit from 15/16. The question is from 06/08 (Higgins Co). That is some time ago, so I accept what you say when you say the question will now ask for slack of there is slack.
But the question Higgins does not ask anything about slack! The examiner does mention it in her answer (the fact that the shadow price is zero means that there is slack) but there was certainly no need to mention that specifically.
(Do appreciate that you can no longer be asked to draw the graph in linear programming questions, as I explain in my free lectures. However you are expected to understand them – you could be given a graph already drawn in the exam.)
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