Uploaded by TheIntegralCALC on 05.06.2011

Transcript:

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.

Yayyyyyyyy!!!!!!!!!!!!!!!!

1

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.

Yayyyyyyyy!!!!!!!!!!!!!!!!

1