Tuesday

September 23, 2014

September 23, 2014

Posted by **Andres** on Thursday, October 13, 2011 at 12:04am.

- Calc -
**Steve**, Thursday, October 13, 2011 at 12:36am1X100

- Calc -
**Reiny**, Thursday, October 13, 2011 at 8:19amlet 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 10:10amI 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 ...

math - a farmer has enough fencing to build 40 feet of fence. He wishes to build...

calculus - Damon help again :) (last one I promise) why is X along the road ...

math - A farmer will make a rectangular pen with 100 feet of fence using pasrt ...

College Cal 1 - A farmer wants to fence off a rectangular field of area 15000 ...

math - A farmer has 1000ft of fence and wishes to enclose the largest possible ...

Pre-Calculas 11 - a farmer wants to build two pens (one for cows, the other for ...

math - If a man is fencing in a rectangular lot of grass next to the road and ...

Calculus - Damon, Help :) A rancher plans to set aside a rectangular region of ...