Applied Optimization with Star Wars Alpacas

Uploaded by TheIntegralCALC on 05.06.2011

Not the Alpacas…
After defeating the evil empire and, saving the universe from utter destruction, Luke
Skywalker settles down as a cost sensitive Alpaca farmer on his home planet of Tatooine.
He’s using a thousand feet of fencing to build a rectangular enclosure along the straight
wall in order to contain the only thing that remains of the empire, a herd of evil storm
trooper Alpacas. Help Luke make the best using of the fencing at find the dimensions that
maximize the area of the pen. Okay. So Luke has a thousand feet of fencing
to build an evil Alpaca pen against the rock wall. Since it has to be a rectangle, it will
look roughly like this. Luke can write the equation of the area as a equals xy, in coupled
width of the pen, x, and the length of the pen, y. If he adds all three sides together,
he gets two x plus y, and since he has a thousand feet of fence to make all three sides, he
knows that two x plus y equals one thousand. When Luke solves this for y, he gets y equals
one thousand minus two x. He knows his area equation, he can replace y with x’s. Using
his Jedi mind tricks, Luke finds the derivative of the area function, sets it equal to zero,
and solves for x. He now quickly solves the other variable that comes the dimensions that maximize the area
of the evil Alpaca pen. PS: If Luke needed to know the area of the
pen itself, he just plugged both dimensions back into the area function.
You gotta love Luke.