Chicken Trouble

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Joined Jan 27, 2019
A chicken farmer had a problem. He could never raise enough chickens to fill his truck for the long trip to market, so the fuel costs for the partial truck reduced his profits to the point where his farm was losing money every year.

Something had to be done, so he got a loan and built another coop to increase production. At the end of the first season he found, to his dismay, that he'd increased production too much! Instead of a full truck he now had one and a quarter truckloads of chickens to take to market.

This situation was much worse than before. Now he had a mostly empty truck and a very expensive second trip to make. He'd depended on selling all the additional chickens to pay off the loan, so he had to do something. He tried to bring all the chickens to market by packing them tightly into the truck but more than half died on the way from the overcrowding and he suffered a great loss. His savings were now almost gone. He needed help!

His friend suggested to him that he go talk to the professors at the new land grant university that was a few miles away. He said that surely those educated folks could help him solve the problem. He figured it was worth a try.

When he arrived, he first tried the engineering department. The engineering professor listened sympathetically to the farmer. "This is no problem", he said, and he took the Chemical Rubber Company handbook off the shelf and found the livestock and poultry packing section. "Here's how you do it", he said, handing the book to the farmer. "But that's how I do it today!", complained the farmer. "Well, then you are doing it right! Industry standard packing, can't get better.", said the engineer.

Un-helped and unhappy, that farmer sought out the math professor. He explained the problem, just as he'd done with the engineer. He wasn't quite sure if the man was actually listening but when he was finished the mathematician became very animated. "What a fantastic problem in topology! I will get some of my grad students working on this right away. Don't worry, we'll find an answer for you!" Quite happy with this turn of events, the farmer went home and slept a little better that night.

A few days later he hadn't heard from the professor so he decided to pay him a visit and see how things were going. He found the professor in his office, making undecipherable marks mixed with numbers in a notebook. When the professor noticed him he was very friendly. "Please come in, it's good to see you!", he said, "we've made fantastic progress!" The farmer was very pleased. "So you have an answer for me?", he asked. "Oh, no, not yet", said the mathematician, "but we've had a breakthrough. Just last night my best graduate student proved that it is possible to put a chicken in a truck!"

This was entirely too much for the poor farmer how had been counting on help from the mathematician. His farm was failing. He would be penniless soon. He was in deep trouble. What was wrong with these academics? Dazed, he wandered out of the office and down the hall. He saw the sign for the Physics department. More because he felt the need to unburden himself than because he expected help, he went in. There he found the physicist, who greeted him warmly.

The farmer went on at length, first describing his problem and then the frustration of dealing with the engineer and the mathematician in trying to get help. The physicist nodded knowingly. "My friend, I am not at all surprised by your trouble with my colleagues. They are both fine men but, frankly, much of the time they just can't see things that are right in front of them" "Take your problem, for example. Something so obvious and trivial and yet they offer you no help."

"Wait", said the farmer, "you mean you know how to solve my problem?" He couldn't help but be hopeful. It seemed he had finally found the right person after all. "Why certainly", said the physicist walking to the blackboard and picking up his chalk, "nothing could be simpler!"

"First, we assume a spherical chicken of uniform density..."