A gardener wants to grow carrots along the side of her house. To protect the carrots from wild rabbits, the plot must be enclosed by a wire fence. The gardener wants to use 20 feet of fence material left over from a previous project. Assuming that she constructs a rectangular plot, using the side of her house as one edge, estimate the area of the largest plot she can construct.

___________square feet.

Question

A gardener wants to grow carrots along the side of her house. To protect the carrots from wild rabbits, the plot must be enclosed by a wire fence. The gardener wants to use  20 feet of fence material left over from a previous project. Assuming that she constructs a rectangular plot, using the side of her house as one edge, estimate the area of the largest plot she can construct.

___________square feet.

anonymous · Answer

Thank you for taking the time to drop by and helping me out:)

anonymous · Answer

This is an optimization problem. Amount of fence used= 2w+l=20. A=lw. A=(20-2w)w. A'=w(-2)+20-2w. Set A' to zero in order to optimize the function. 

0=-4w+20 -> w=5 -> when w= 5 l must equal 10 as 2w+l=20

anonymous · Answer

good?

anonymous · Answer

hmmm im still working on it...

anonymous · Answer

the key to optimization problems is that you almost always need to substitute something.

anonymous · Answer

hmmm so I would use ...?

anonymous · Answer

oh wait you already solved it didn't you heheh...hold up let me check it on wiley plus this math system ...

anonymous · Answer

so were substituting -- the constraint of this function -- 2w+l = 20.

anonymous · Answer

I tried 10 for the answer and it didnt work >.< hehe i must have done something wrong

anonymous · Answer

Thank you!!! it was 50 right:) lol I just got back to earth, thanks...

anonymous · Answer

booyah first answer, first medal. glad to help you out.

anonymous · Answer

Nice, first medal:) YW.