A farmer is trying to build a chicken coop to hold all of his chickens. He has 460 meters of fence to use to build the coop and one side of the coop will be placed against the barn. Draw a picture to represent the situation. Then write a function representing the area of the chicken coop. What are the dimentions length and width of the coop with the larget area? What is the maximum area?

Question

anonymous · Answer

Geez you're really testing me here. It's Calc 1 all over again.

anonymous · Answer

thats what math im in lol.

anonymous · Answer

I need to head to dinner since I have a paper due tomorrow, but I'll tell you what you need to do. You need to make two functions, one that represents area, one that represents perimeter. Your equation for perimeter should be equal to 460.

I'll be back on in half an hour, hopefully once you get your area function and perimeter function, it shouldn't be too hard to solve for length and width.

As a hint, Let x = l (length).

radar · Answer

Your perimeter may be more than 460 as the length of the barn comes into play it is part of the perimeter.

I would let x be the length of the barn.  Then the 460 meters of fence will make up the remaining three sides.  One of the three sides will also be x (side opposite the barn.  the other two sides will be (460-x)/2 each. The area will be A=x*(460-x)/2 or(460x-x^2)/2  Now differentiate that and set to 0 and solve.

radar · Answer

A=-1/2 x^2+230 differntiating :  -x+230 . for max/min let equal 0.
0=-x+230, solve for x, x=230 so the barn is 230meters, the opposite side is 230 meters, the other 2 sides are (460-230)/2=115 meters each.

radar · Answer

Messed up equation for area omitted the x at the end of 230 in equation for Area.  Do you follow?