garden uses stream as 1 side, 20 ft fencing available; find

[vkenny]

Hi everyone. I'm new here. i doing my homework and i didnt how to do this. i hope someone can help me.

Janice wants to fence in a small garden area next to a stream. If she has 20 feet of fencing materials and doesnt fence the side bordering the stream, find the dimensions that will yield the maximum area and then find the maximum area she can enclose.

this is what i got so far
x+20y=20

A=xy

 

[Deleted member 4993]

Re: Word problem

Hi everyone. I'm new here. i doing my homework and i didnt how to do this. i hope someone can help me.

Janice wants to fence in a small garden area next to a stream. If she has 20 feet of fencing materials and doesnt fence the side bordering the stream, find the dimensions that will yield the maximum area and then find the maximum area she can enclose.

this is what i got so far
x+20y=20 ............................................(1)

A=xy..................................................(2)

Since you posted this problem in Advanced Math section - I assume you know calculus - and hence know how to find maximum of a function.

First you need to define EXPLICITLY - what is 'x' and what is 'y'.

In equation (1) - why do you have a term '20y'?

If 'y' is the perpendicular to the stream - then that should be '2y'.(This is where definition would be useful - little mistakes can be overcome easily for the tutors).

After correcting it - solve for 'x'.........................................................(3)

Then replace 'x' in (2) using (3).

Then differentiate 'A(y)' and find the condition for maximum.

If you are still stuck, please share with us your work/thoughts - so that we know where to begin to help you.

 

[vkenny]

Re: Word problem

Hi everyone. I'm new here. i doing my homework and i didnt how to do this. i hope someone can help me.

Janice wants to fence in a small garden area next to a stream. If she has 20 feet of fencing materials and doesnt fence the side bordering the stream, find the dimensions that will yield the maximum area and then find the maximum area she can enclose.

this is what i got so far
x+20y=20 ............................................(1)

A=xy..................................................(2)

Since you posted this problem in Advanced Math section - I assume you know calculus - and hence know how to find maximum of a function.

First you need to define EXPLICITLY - what is 'x' and what is 'y'.

In equation (1) - why do you have a term '20y'?

If 'y' is the perpendicular to the stream - then that should be '2y'.(This is where definition would be useful - little mistakes can be overcome easily for the tutors).

After correcting it - solve for 'x'.........................................................(3)

Then replace 'x' in (2) using (3).

Then differentiate 'A(y)' and find the condition for maximum.

If you are still stuck, please share with us your work/thoughts - so that we know where to begin to help you.

thank you for helping me. I'm only in precalculus.
so this is what I've got
x+2y=20
x=20-2y
since A=xy
A=(20-2y)y
so what i should do next. do i need to graph it

 

[Deleted member 4993]

Re: Word problem

thank you for helping me. I'm only in precalculus.
so this is what I've got
x+2y=20
x=20-2y
since A=xy
A=(20-2y)y <<< This is an equation of a parabola - where is it's vertex - what is the value of(y,A) at that point?
so what i should do next. do i need to graph it