Solving a Modelling Problem Involving a Sink

[Harriet12]

I'm dong a question that involves a sink. The aim is to determine the dimensions of the sink (width and length) which will provide the greated cross-sectional area by modelling using an equation. Here's the catch: you are only allowed a sheet of stainless steel that it 60cm wide and a 5cm overlap has to be allowed for on either side of the sink.

So far I've figured this:
when:
c=cross-sectional ares
a=area
l=length
w=width

a= l x w
c=a
so c= l x w

w=60-(10+2L)

therefore:
c= L[60-(10+2L)]
c=60L-10L+2L^2

etc etc. when applying this formula like this:

L = c/w
L = L[60(10+2L)] / 60(10+2L)

eventually L turns out to be 0 (duh i didnt give it a value)
But here comes my question: is there a flaw in my formula or am i completely off-track? please help!

 

[Harriet12]

Here is the picture...

 

[Tide]

Harriet,

Perhaps you would clarify exactly what problem you are attempting to solve. I don't understand what you're looking for from what you wrote.

 

[mathmike]

lets see what we have

2l + w + 10 = 60

a = l * w

w = 50 - 2l

so a = (50 - 2l) * l

da/dl = 50 - 4l

set = to 0

50 - 4 * l = 0

l = 12.5

plug it in the area equation

50(12.5) - 2(12.5) ^2 = 312.5

you can do the rest yes