Calculus Word problem

[dear2009]

Hey everyone,


You need to fence in a rectangular enclosure. The side along the street needs a brick wall, which costs $50/foot, while the other three sides may be constructed of wood, and cost $20/foot. If the total area enclosed is to be 10,000 square feet, what rectangular dimensions will yield the minimum cost for the fence, and what is the minimum cost?


This is what I did

BW = 10,000
W = 10,000/B

C = 50B + 20(2W + B)
C = 50B + 20W + 10B
C = 70B + 40W

C = 70B + 20(10,000)
C = 70B +200,000
70B^2 = 400,000B
70B = 400,000B

when I got my final answer it was $10,583.00 but I got the answer wrong

these are the following answers that were given in the problem
$10,583.00
$10,583.01
$10,583.02
$10,583.03
$10,583.04

Can somebody show me the most accurate answer (In the hundreds place)? Thanks in advance

 

[tkhunny]

BW = 10,000 -- Good.
W = 10,000/B -- Good.

C = 50B + 20(2W + B) -- Good.
C = 50B + 20W + 10B -- Very Bad. Do this again.
C = 70B + 40W -- How did you get this from the previous line?

C = 70B + 20(10,000) -- It changed back to 20 again? Shouldn't that be (10,000 / b)?
C = 70B +200,000 -- The 'b' remains missing from the denominator.
70B^2 = 400,000B -- You just pulled another 'b' out of your pocket?
70B = 400,000B -- Ant then you threw it away again.

This makes very little sense. You need to think about what you are doing and stop trying to follow some procedure. It has to make sense to YOU.

BW = 10,000
W = 10,000/B

C = 50B + 20(2W + B)
C = 50B + 40W + 20B -- Repaired
C = 70B + 40W -- Really, how did you get this?

C = 70B + 40(10,000/B) -- Substituting the ENTIRE expression, rather than ignoring the denominator.
C = 70B + 400,000/B -- Repaired
70B^2 = 400,000B -- You lost me, here. What was your motivation for this?

Perhaps dC/db = 70 - 400000/(B^2)

Now what?

Slow down. Be careful and deliberate. Make sure YOU know what you are doing.