SOLUTION: I would like to fence in a rectangular area in my back yard for my dog. I would like to use chain link fencing, which is only $7 per lineal foot, for both sides and the front. The

Question 1037299: I would like to fence in a rectangular area in my back yard for my dog. I would like to use chain link fencing, which is only $7 per lineal foot, for both sides and the front. The guy that lives behind me has a dog, and if the two of them see each other, they will be barking all of the time. So, I will need to use solid redwood fencing at $28 per lineal foot to do the back wall.
I would like the area to be 300 square feet, but do it at a minimum cost. How much of the redwood fencing will I need to buy?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x=sides
y=front and back
xy=300, area
Cost=7(2x+y)+28y=14x+35y
y=300/x
cost is 14x+10500/x
Take the derivative and set it equal to zero.
14-10500/x^2=0
14=(10500/x^2)
14x^2=10500
x^2=750
x=27.38 feet.
y, the amount of redwood fencing, is 10.96 feet. Total cost is 65.72@$7=$460.04 plus 10.96*28=306.88=$766.92
check with 25 and 12 for area of 300
62 feet of chain ($434)
12 feet of redwood (336), total is $770.
30 and 10--90*$7=$630 and 10*$28=$280, for total of $910.

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