Sunday, January 29, 2006

First Row, Second Person

As soon as this incident happened on last wednesday, I thought "I gotta blog this." But it wasn't until today that I am able to do it. Blame it on my busy schedule or Blogger's Syndrome*.

Anyway, the incident I want to discuss happened in the Operations Research class of wednesday. For those not aware of it, its mostly Linear Programming and similar other optimiation technique. But I should add a disclaimer here that even I am not fully aware of it as I have just begun this course. Now I took this course because I had already taken a course names 'Design Optimization' in which we studied Linear Programming. I thought that I have a better chance at this subject as compared to others in whom I was told that there's won't be anything worthwhile to learn or the professor gave really bad grades.

Things seemed to work perfectly well till the wednesday's class where it was all a jolly ride for me and Suman while the others fretted out to understand the concepts. Thing were going on pretty well when the professor decided to start a new topic, on the principle of duality in LP. She told how every LP problem has a dual; how every maximization problem's dual is a minimization one. Then to elucidate her point, she told that a profit maximization problem is also modelled by a cost minimization problem. Then she told us to turn back the pages and open a problem that she had taught long ago. She revised the problem and asked us to reformulate the dual of the problem. The first part, that of redefining the objective function was easy as we just had to swap the variables from production rate of materials to unit cost of production. This she even did herself. No prize for guessing that she asked us to reformulate the constraints for the problem. Now as I had already done a course attributing to which I was able to identify all the constraints, I went ahead with dictating them while others stared with a halu look on their face. But things weren't as pretty as I thought. As soon as she was finished writing the equations, she turned back and said, "Now will the person who said all these please stand up and explain how he got them from a physical significance point of view". To say the least, I was bowled out. In the whole course of DO, we were just given a problem which we transformed to the dual by taking transpose and changing the variables. Here was a new problem and I was short of time. I thought that I should say something vague to keep myself off the controversy and for that I had to find something to say by the time the professor identified who was the person. I thought this would be easy as I had to just re-engineer the question as I already knew the answer. All I had to do was to say whatever was written in the equation in plain english and the truth shall set me free. But unfortunately, luck wasn't on my side. I couldn't understand what vague statement the equation meant as I tried to ignore the classroom making some unfriendly noise.

"Who was it?", the professor demanded. Many people (must have been over 40) replied in a loud voice "Ma'am..first row, second person." Obviously it was be.

"Yes", she said talking to me, "please explain how you got this result". I was still turning pages trying to understand what the statement meant. At the same time, I told my neighbours (Vikas and Suman) in a hushed tone that they should help me if they got it figured out. Sadly noone did. The seconds passed like ages and the silence grew very uncomfortable. Then she started herself "See, the person who got this was able to say as he had already done a course in Linear Programming. I just wanted to know if he knew how to arrive at the solution". The truth was out and I was feeling a bit relieved. She then went on to explain what the constraints meant in real life. What I was expecting to be an insight soon turned like a joke. By reverse engineering the equation, she came up with the 'statement' that said "Cost of production >= Profit". I couldn't understand the meaning. Even I was able to get that statement in those precious minutes, but had to discard this as a rubbish theory. I pressed to find out how and was eventually told by her that had the problem been one in which we were to reformulate the dual, something would have been given to arrive at this conclusion. I was still not convinced. I tried to find out if the problem was indeed a dual, there should have been data in it already. What seemed like an anti-climax, she told that even she didn't knew how this came!

Neat, huh.

*Blogger's Syndrome - A condition in which a blogger who has been active for a while suddenly stops posting, eventhough most of the times he checks others' blogs and also has something to say. Surprisingly, everyone suffering from it accepts it but defends it in various fashion. Although its largely attributed to busy work schedule, recent researches have shown that there might be more to it.

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