Posted by Andres on Thursday, October 13, 2011 at 12:04am.
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  Steve, Thursday, October 13, 2011 at 12:36am
1X100

Calc  Reiny, Thursday, October 13, 2011 at 8:19am
let the length be x, let the width be y
xy = 100
y = 100/x
cost = 34x + 16x + 16(2y) = 34x + 48y
= 34x + 48(100/x)
d(cost)/dx = 34  4800/x^2 = 0 for a minimum cost
34 = 4800/x^2
x^2 = 4800/34
x = appr. 11.88 ft
pen is 8.42 by 11.88 ft, with the 11.8 ft along the road
minimum cost = 34x + 4800/x = 807.96
check:
take x = 12 , cost = 808
take x = 11 , cost = 810.36
take x = 1 (Steve's answer) , cost = 4834
take x=100 , cost = 3448
The answer of 11.88 by 8.42 is correct for a min cost of $807.96

Calc  Steve, Thursday, October 13, 2011 at 10:10am
I was joking with the 1x100. Also, I notice that your solution is incorrect, because 16(2y) is not 48y.
The correct solution has appeared elsewhere as 8x12.5
Answer This Question
Related Questions
 Calc  A farmer wishes to enclose a rectangular pen with area 100 square feet ...
 calc  A farmer wishes to enclose a rectangular pen with area 100 square feet ...
 Calculus Follow Up  A farmer wishes to build a fence for 6 adjacent rectangular...
 Calculus Word Problem  A farmer wishes to build a fence for 6 adjacent ...
 Calculus  ABC Daycare wants to build a fence to enclose a rectangular ...
 Calculus  Optimization  A fence is to be built to enclose a rectangular area ...
 Math  A fence is to be built to enclose a rectangular area of 310 square feet. ...
 Math  A fence is to be built to enclose a rectangular area of 310 square feet. ...
 Calculus  A fence is to be built to enclose a rectangular area of 310 square ...
 Calculus 1  A fence is to be built to enclose a rectangular area of 220 square ...
More Related Questions