Posted by Lisa on Sunday, March 10, 2013 at 8:44pm.
We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?
I am not even sure how to start though I know I am supposed to calculate the derivative of the setup. Thank you

Maximum Area  Steve, Sunday, March 10, 2013 at 8:53pm
if the yard has dimensions x and y, and side x is parallel to the building, then the fencing used is
x+2y = 900
The area is
a = xy = (9002y)*y = 900y  2y^2
da/dy = 900  4y
da/dy=0 when y=900/4 = 225
so, x = 9002y = 450
the yard is thus 450 by 225

Maximum Area  Lisa, Sunday, March 10, 2013 at 9:06pm
I do not think I made it clear sir. The part where I was stuck was where 100 ft. of the building is covered by the side of the yard.
___________________
 yard 
 

} building {

the building length is 100 feet
Sorry for any confusion this caused.

Maximum Area  Lisa, Sunday, March 10, 2013 at 9:08pm
As the text drawing did not come out clear I hope this may clarify what I meant.
imgur /F5NJVqp

Maximum Area  Steve, Monday, March 11, 2013 at 1:21am
You're right  you did not make it clear that the building was only 100 feet wide.
If the building on;y covers 100 feet of the side x, then
x+(x100)+2y = 900
2x+2y=1000
x = 500y
and follow the same steps above.
If I still have it wrong, then just draw yourself a diagram and label the various parts, making sure all the fence sections add up to 900. Then substitute for x or y in the formula a=xy.
Answer This Question
Related Questions
 Maximum AreaCalculusEdit  We have 900 ft of fencing and we want to construct ...
 AP Calculus  The management of a large store has 1600 feet of fencing to fence ...
 math  Susan's back yard is rectangular with dimensions 39 yd. by 71 yd. Carlos'...
 math  Chris wants to make an enclosed rectangular area for a mulch pile. She ...
 calculus help  Farmer Brown wants to fence in a rectangular plot in a large ...
 Math, Quadratic Functions  A rectangular chicken yard was built against an ...
 PreAlgebramath  Mr.jones bought 20 yards of fencing to make pen for dog pen ...
 5th grade math  suppose you are building a fence for a garden in your yard. ...
 Precalculus  Combined area of 1680ft^2 for 4 identical rectangular corrals. ...
 math  Ms. Jacobs is planning to put a fence around a rectangular part of her ...
More Related Questions