Posted by Andres on Wednesday, October 12, 2011 at 8:04pm.
A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What dimensions for the pen will minimize the cost to the farmer. What is the minimum cost?

calc  bobpursley, Wednesday, October 12, 2011 at 8:14pm
Area= R*W where road fence is R, W is the length perpendicular to the Road.
Cost= 34R+16(R+2W)= 34Area/W+ 16(Area/W+2W)
dCost/dw= 34*100/W^2+ 16(100/W^2+2)=0
0=34001600+32W^2
W= sqrt (5000/32)
L= 100/W
check my math.

calc  Steve, Wednesday, October 12, 2011 at 8:16pm
let there be length a and width b, with side a along the road.
b = 100/a
cost is a*34 + a*16 + 2*100/a * 16
c = 50a + 200/a
c' = 50  200/a^2
c' = 0 when a = 2
so, the minimum cost is 100 + 100 = 200
a 2' wide pen? Is he housing gerbils?

calc  Steve, Thursday, October 13, 2011 at 12:07am
My bad  bobpursley is correct. The road length is 8, width is 12.5
using my notation,
c = 50a + 3200/a
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