SOLUTION: Choose one of the following (circle your choice); determine the equations and solve the problem below. (Remember to define variables, include a diagram or sketch and interpret you

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Question 1181411: Choose one of the following (circle your choice); determine the equations and solve the problem below.
(Remember to define variables, include a diagram or sketch and interpret your answers in relation to the problem).
A) A farmer is constructing a pig pen and is using his barn wall as one side of the pen. If he has 32 m of fencing and wants to use it all, determine the dimensions that will produce the maximum area of the pen.
Found 2 solutions by ikleyn, Solver92311:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

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Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!

.
Length of Fence:

Length of Pen as a function of width:

Area of pen:

Area of pen as a function of width:

Take the first derivative:



Set the derivative equal to zero to find an extremum:





Take the second derivative:



Therefore in the domain of A, and therefore the one extremum is guaranteed to be a maximum.

If the maximum area is obtained when , then calculate to get the other dimension.


John

My calculator said it, I believe it, that settles it

From
I > Ø