SOLUTION: A petting zoo is working to construct a rectangular pen. The pen will have 1 partition to create separate spaces for goats and pigs. The petting zoo has 1000 feet of fencing to use

Question 1085521: A petting zoo is working to construct a rectangular pen. The pen will have 1 partition to create separate spaces for goats and pigs. The petting zoo has 1000 feet of fencing to use.
a. Write an area function (A(x)) that gives the area of the enclosure as a function of the length of a partition, x.
b. Find the dimensions of the pen that will provide the greatest area.
c. What is the maximum area that can be enclosed?
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
x, a dimension of the whole pen
y, other dimension of the whole pen

Total fence length 1000 feet, and choosing x as the length of the one partition piece, for making two enclosures,

A(x) would be a parabolic function, with vertex as a maximum. This x value for maximum will occur in the exact middle of the two zeros of A.
, to find the two zeros.

and the other zero is
.

Maximum A will be at , feet.
RELATED QUESTIONS
A petting zoo is working to construct a rectangular pen. The pen will have 2 partitions... (answered by josmiceli)

A petting zoo is working to construct a rectangular pen. The pen will have 3 partitions... (answered by ankor@dixie-net.com)

Philip wants to construct a dog pen at the back of his garage. He will use the wall of... (answered by Boreal)

A pen is to be formed by enclosing a rectangular fenced area in an open field. The pen... (answered by ikleyn)

300 ft of fencing is available to fence a rectangular pen where one side will be ordered... (answered by rfer)

problem solving using quadratic functions: Philip wants to construct a dog pen at the (answered by solver91311)

A rancher is going to construct a new rectangular pen for his emu farm. If he has 5200... (answered by rfer)

Fred wants to construct a rectangular chook pen, using a barn for one of the sides... (answered by lwsshak3)

Bobby is planning on making a rectangular pen for the class pig, "Bacon". He would like... (answered by josmiceli)