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  LiveWire / Teen Forums / School & Homework Connection / Viewing Topic

Math Problem Help
Easy Problem
Replies: 3 — Last Post Nov. 4 9:06pm by hithere
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( Anonymous )

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The problem:
You have a 3000 sq. foot botanical garden where three sides consist of shrubs that cost $25 per foot and one side consists of shrubs that are $10 per foot. What's the minimum total cost?

I'm not entirely sure how to set this up...
I dunno I'm confused...
75x + 10x = x*(3000-x)
???

7:04 pm on Nov. 4, 2009
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Rachelw


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10x+25x*3000= total cost.

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7:06 pm on Nov. 4, 2009 | Joined: Oct. 2008 | Days Active: 227
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( Anonymous )

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Quote: from Rachelw at 5:06 pm on Nov. 4, 2009
10x+25x*3000= total cost.

...I'm not sure that's right...

7:10 pm on Nov. 4, 2009
hithere


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area[x,y]=3000=xy→y=3000/x
cost[x]=25*2x+25y+10y=50x+25(3000/x)+10(3000/x)=50x+75000/x+30000/x=50x+105000/x

find critical points:
d(cost)/dx=50-105000/x^2=0→50=105000/x^2→50x^2=105000→x^2=2100→x=2100^(1/2)

find values of cost function at critical point and endpoints:
cost[2100^(1/2)]=50[2100^(1/2)]+105000/[2100^(1/2)]≈4582.58
lim[x→0]cost[x]=+∞
lim[x&rarl∞]cost[x]=+∞

thus the lowest value of the cost function is 4582.58

Post edited at 5:05 am on Nov. 5, 2009 by hithere

9:06 pm on Nov. 4, 2009 | Joined: Dec. 2005 | Days Active: 1,035
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